{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 02 - Randomized Experiments and Stats Review\n",
    " \n",
    " \n",
    "## Brute Force Independence with Randomization\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An A/B Testing Example\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:29.347488Z",
     "start_time": "2023-09-01T17:14:28.695287Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "pd.set_option('display.max_rows', 5)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:29.363096Z",
     "start_time": "2023-09-01T17:14:29.349423Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gender</th>\n",
       "      <th>cross_sell_email</th>\n",
       "      <th>age</th>\n",
       "      <th>conversion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>short</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>short</td>\n",
       "      <td>27</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>321</th>\n",
       "      <td>1</td>\n",
       "      <td>no_email</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>322</th>\n",
       "      <td>1</td>\n",
       "      <td>long</td>\n",
       "      <td>24</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>323 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     gender cross_sell_email  age  conversion\n",
       "0         0            short   15           0\n",
       "1         1            short   27           0\n",
       "..      ...              ...  ...         ...\n",
       "321       1         no_email   16           0\n",
       "322       1             long   24           1\n",
       "\n",
       "[323 rows x 4 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd # for data manipulation\n",
    "import numpy as np # for numerical computation\n",
    "\n",
    "data = pd.read_csv(\"./data/cross_sell_email.csv\")\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:29.371157Z",
     "start_time": "2023-09-01T17:14:29.364511Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gender</th>\n",
       "      <th>age</th>\n",
       "      <th>conversion</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cross_sell_email</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>long</th>\n",
       "      <td>0.550459</td>\n",
       "      <td>21.752294</td>\n",
       "      <td>0.055046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>no_email</th>\n",
       "      <td>0.542553</td>\n",
       "      <td>20.489362</td>\n",
       "      <td>0.042553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>short</th>\n",
       "      <td>0.633333</td>\n",
       "      <td>20.991667</td>\n",
       "      <td>0.125000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    gender        age  conversion\n",
       "cross_sell_email                                 \n",
       "long              0.550459  21.752294    0.055046\n",
       "no_email          0.542553  20.489362    0.042553\n",
       "short             0.633333  20.991667    0.125000"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(data\n",
    " .groupby([\"cross_sell_email\"])\n",
    " .mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:29.383056Z",
     "start_time": "2023-09-01T17:14:29.373475Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gender</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cross_sell_email</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>long</th>\n",
       "      <td>0.015802</td>\n",
       "      <td>0.221423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>no_email</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>short</th>\n",
       "      <td>0.184341</td>\n",
       "      <td>0.087370</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    gender       age\n",
       "cross_sell_email                    \n",
       "long              0.015802  0.221423\n",
       "no_email          0.000000  0.000000\n",
       "short             0.184341  0.087370"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = [\"gender\", \"age\"]\n",
    "\n",
    "mu = data.groupby(\"cross_sell_email\")[X].mean()\n",
    "var = data.groupby(\"cross_sell_email\")[X].var()\n",
    "\n",
    "norm_diff = ((mu - mu.loc[\"no_email\"])/\n",
    "             np.sqrt((var + var.loc[\"no_email\"])/2))\n",
    "\n",
    "norm_diff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Ideal Experiment\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " \n",
    "## The Most Dangerous Equation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:30.685676Z",
     "start_time": "2023-09-01T17:14:29.384770Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import seaborn as sns\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import style\n",
    "from cycler import cycler\n",
    "import matplotlib\n",
    "\n",
    "default_cycler = (cycler(color=['0.1', '0.5', '1.0']))\n",
    "\n",
    "color=['0.3', '0.5', '0.7', '0.9']\n",
    "linestyle=['-', '--', ':', '-.']\n",
    "marker=['o', 'v', 'd', 'p']\n",
    "\n",
    "plt.rc('axes', prop_cycle=default_cycler)\n",
    "\n",
    "matplotlib.rcParams.update({'font.size': 18})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:30.706628Z",
     "start_time": "2023-09-01T17:14:30.687207Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>school_id</th>\n",
       "      <th>number_of_students</th>\n",
       "      <th>avg_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>16670</th>\n",
       "      <td>2007</td>\n",
       "      <td>33062633</td>\n",
       "      <td>68</td>\n",
       "      <td>82.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16796</th>\n",
       "      <td>2007</td>\n",
       "      <td>33065403</td>\n",
       "      <td>172</td>\n",
       "      <td>82.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14636</th>\n",
       "      <td>2007</td>\n",
       "      <td>31311723</td>\n",
       "      <td>222</td>\n",
       "      <td>79.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17318</th>\n",
       "      <td>2007</td>\n",
       "      <td>33087679</td>\n",
       "      <td>210</td>\n",
       "      <td>79.38</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       year  school_id  number_of_students  avg_score\n",
       "16670  2007   33062633                  68      82.97\n",
       "16796  2007   33065403                 172      82.04\n",
       "...     ...        ...                 ...        ...\n",
       "14636  2007   31311723                 222      79.41\n",
       "17318  2007   33087679                 210      79.38\n",
       "\n",
       "[10 rows x 4 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"data/enem_scores.csv\")\n",
    "df.sort_values(by=\"avg_score\", ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:30.813067Z",
     "start_time": "2023-09-01T17:14:30.708131Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Number of Students of 1% Top Schools (Right)')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data = (df\n",
    "             .assign(top_school = df[\"avg_score\"] >= np.quantile(df[\"avg_score\"], .99))\n",
    "             [[\"top_school\", \"number_of_students\"]]\n",
    "             .query(f\"number_of_students<{np.quantile(df['number_of_students'], .98)}\")) # remove outliers\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "ax = sns.boxplot(x=\"top_school\", y=\"number_of_students\", data=plot_data)\n",
    "\n",
    "plt.title(\"Number of Students of 1% Top Schools (Right)\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:30.975794Z",
     "start_time": "2023-09-01T17:14:30.814539Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'ENEM Score by Number of Students in the School')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "q_99 = np.quantile(df[\"avg_score\"], .99)\n",
    "q_01 = np.quantile(df[\"avg_score\"], .01)\n",
    "\n",
    "plot_data = (df\n",
    "             .sample(10000)\n",
    "             .assign(Group = lambda d: np.select([(d[\"avg_score\"] > q_99) | (d[\"avg_score\"] < q_01)],\n",
    "                                                 [\"Top and Bottom\"], \"Middle\")))\n",
    "plt.figure(figsize=(10,5))\n",
    "sns.scatterplot(y=\"avg_score\", x=\"number_of_students\", data=plot_data.query(\"Group=='Middle'\"), label=\"Middle\")\n",
    "ax = sns.scatterplot(y=\"avg_score\", x=\"number_of_students\", data=plot_data.query(\"Group!='Middle'\"), color=\"0.7\", label=\"Top and Bottom\")\n",
    "\n",
    "plt.title(\"ENEM Score by Number of Students in the School\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  The Standard Error of Our Estimates\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:30.987374Z",
     "start_time": "2023-09-01T17:14:30.976905Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cross_sell_email\n",
       "long        109\n",
       "no_email     94\n",
       "short       120\n",
       "dtype: int64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"./data/cross_sell_email.csv\")\n",
    "\n",
    "short_email = data.query(\"cross_sell_email=='short'\")[\"conversion\"]\n",
    "long_email = data.query(\"cross_sell_email=='long'\")[\"conversion\"]\n",
    "email = data.query(\"cross_sell_email!='no_email'\")[\"conversion\"]\n",
    "no_email = data.query(\"cross_sell_email=='no_email'\")[\"conversion\"]\n",
    "\n",
    "data.groupby(\"cross_sell_email\").size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:30.993805Z",
     "start_time": "2023-09-01T17:14:30.990856Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SE for Long Email: 0.021946024609185506\n",
      "SE for Short Email: 0.030316953129541618\n"
     ]
    }
   ],
   "source": [
    "def se(y: pd.Series):\n",
    "    return y.std() / np.sqrt(len(y))\n",
    "\n",
    "print(\"SE for Long Email:\", se(long_email))\n",
    "print(\"SE for Short Email:\", se(short_email))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:30.998176Z",
     "start_time": "2023-09-01T17:14:30.995297Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SE for Long Email: 0.021946024609185506\n",
      "SE for Short Email: 0.030316953129541618\n"
     ]
    }
   ],
   "source": [
    "print(\"SE for Long Email:\", long_email.sem())\n",
    "print(\"SE for Short Email:\", short_email.sem())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Confidence Intervals\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:31.094364Z",
     "start_time": "2023-09-01T17:14:30.999382Z"
    }
   },
   "outputs": [],
   "source": [
    "n = 100\n",
    "conv_rate = 0.08\n",
    "\n",
    "def run_experiment(): \n",
    "    return np.random.binomial(1, conv_rate, size=n)\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "experiments = [run_experiment().mean() for _ in range(10000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:31.214686Z",
     "start_time": "2023-09-01T17:14:31.095655Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd451a4bc10>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "freq, bins, img = plt.hist(experiments, bins=20, label=\"Experiment Means\", color=\"0.6\")\n",
    "plt.vlines(conv_rate, ymin=0, ymax=freq.max(), linestyles=\"dashed\", label=\"True Mean\", color=\"0.3\")\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:31.287972Z",
     "start_time": "2023-09-01T17:14:31.216097Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([92.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "         0.,  0.,  0.,  0.,  0.,  0.,  8.]),\n",
       " array([0.  , 0.05, 0.1 , 0.15, 0.2 , 0.25, 0.3 , 0.35, 0.4 , 0.45, 0.5 ,\n",
       "        0.55, 0.6 , 0.65, 0.7 , 0.75, 0.8 , 0.85, 0.9 , 0.95, 1.  ]),\n",
       " <BarContainer object of 20 artists>)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.hist(np.random.binomial(1, 0.08, 100), bins=20)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:31.381464Z",
     "start_time": "2023-09-01T17:14:31.289700Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd451c295d0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hw4dz5MgRq+MolSkTJkzAycmJ8uXL8+mnn7J//35GjRqVdjxonTp1+P7779m6dSv169cnNDQUAG9v77QvWi1atCAxMZFz587d9tyjRo1ixIgRLFy4kEceeYSPP/6Y4cOHZ5jj1t50BweH2/as3+oaPXr0KJMnT2b9+vXs3r2bli1bcv36dZycnNi6dSsdOnTgq6++olmzZgB88MEHjBkzhuPHj1OtWjXOnz+fvT+4u7BpcSYizUTkNxE5JCJDM3i8rYjsFpGdIhItInXTPXZMRH659Zgtcyql7JcxhqFDh3L06FGCgoIICgqyOpJNOTo6UqdOHW7evEmXLl1ITEy0OpJSD+3MmTMAJCQkMHHiRPr16wfAqVOnMMYAsHXrVpKTkylSpEhau4MHD3LixAkaNGhAXFwcDg4OiAjXr19/oByXL1/Gw8MDHx8fTp8+zZo1awC4evUqly5dokWLFkybNo2dO3cCcPjwYWrVqsWoUaMoWrTobd2xtmSzY85ExBGYATQBYoBtIrLCGPNrutXWAyuMMUZEqgKLgQrpHm9kjLm9hFZK5Suff/45X375JYGBgbn+zMzM8vb2pnr16mzfvp2BAwfqPJwqS3x8fLL1+CgfH5+Hfo5JkyaxcuVKkpOT6d+/P4899hgAS5YsYdasWTg5OVGgQAEWLVqEiKS1GzFiBGPHjgWgS5cutGvXjunTpzNq1KgHyhEeHk716tWpVKkSISEhREVFAXDlyhXatm3L9evXMcYwdepUAF555RUOHjyIMYbGjRsTHh7+MD+GTJNbFWu2P7FIHeBNY8wTqfeHARhjxt9j/Y+NMRVT7x8DIrJSnEVERJjoaN3JplRe8dtvv9GiRQs8PDyoXLnybd+o84MtW7YQGxvL9OnTeeqpp6yOo+zUvn37qFixotUx1H1k9HsSke3GmIg717XlV9ASQPr9fzGpy+4M9qSI7AdWAb3SPWSAb0Rku4j0vduLiEjf1C7R6LNnz2ZTdKWU1eLi4ujXrx8iQqlSpfJdYQYQERGBu7s7Q4YM4Y8//rA6jlIqh9iyOJMMlv1lN50xZpkxpgLQDhid7qEoY0wNoDkwQEQyHGDEGPOhMSbCGBPh6+ubDbGVUvZg9OjRHDx4kJIlS+b548zu5tbxZ4mJiXTt2hVb9XQopeyLLYuzGCD9O2ogcOJuKxtj/geUEZGiqfdPpF6fAZYBkbaLqpSyJz/88APz58+nWLFihISE4OjoaHUky/j4+FC5cmWOHj3KxIkTrY6jlMoBtizOtgGhIhIsIi5AZ2BF+hVEpKykHvknIjUAF+C8iHiIiFfqcg+gKbDHhlmVUnbi2rVrDB48GC8vL0qVKkWBAgWsjmS5MmXKUKhQIWbOnMmBAwesjqOUsjGbFWfGmCTgeWAtsA9YbIzZKyL9RKRf6modgD0ispOUMzs7mZT99v7ADyKyC9gKrDLG/MdWWZVS9mPs2LHExMQQGBiIv7+/1XHsgogQGRmJMYbevXtr96ZSeZxNp28yxqwGVt+x7IN0tycCf9lPb4w5AuTM+apKKbvx448/Mm/ePIoXL07p0qXzxbAZmeXh4UGlSpX45ZdfePvtt3n11VetjqSUshGdW1MpZReuXbvGP//5T+3OvIeyZcty/PhxZs6cSfv27dNGWVcqvUmTJhEbG5ttz1eiRIl7TjieGcYYXnvtNb744gscHR3p378/AwcO5NKlSzz99NP88ccfJCUlMXjwYJ555hnOnj3Lk08+ycWLFxkzZkzatE5t27Zl1qxZFC9ePBu2zH5pcaaUsgvjxo0jJiaG8uXLa3fmXYgItWrVYt26dfTq1Yv//e9/tw3YqRRAbGxstp7hnB2j4s+dO5fjx4+zf/9+HBwc0mYMmDFjBmFhYXz99decPXuW8uXL061bNxYuXEiPHj3o3LkzzZo1o127dnz99dfUqFEjzxdmoHNrKqXswE8//cTcuXMpVqwYwcHB2p15D7e6N48cOcKkSZOsjqNUpsyaNYuRI0em/W/7+fkBKV84rly5gjGGq1evUrhwYZycnHB2diY+Pp6EhIS0eTGnTZt2zz14PXv2pH///jRq1IiQkBC+++47evXqRcWKFenZs2faev379yciIoJKlSrxxhtvpC0fOnQoYWFhVK1alcGDBwPwxRdfULlyZcLDw6lfP8MRvWxC95wppSyVkJDAkCFDtDszC251b86YMYMuXbrk23HglP2YMWMG8+fPx8XFhWeeeYZ69eqxZMkSGjRowKOPPsrhw4f5/PPPWbZsGb6+vrz77ruEhoby/PPP06ZNG4oXL86VK1f4/PPPcXBwoGvXrnTt2pX58+czceJEZs6cSffu3XF3d79njgsXLrBhwwZWrFhB69at+fHHH5kzZw41a9Zk586dVKtWjbFjx1K4cGFu3rxJ48aN2b17N4GBgSxbtoz9+/cjImnTX40aNYq1a9dSokSJbJ0S637066lSylIzZ87k6NGjFCtWTLszM0lEqFmzJjdv3qR///5Wx1GK48ePpxVCGzdupHXr1sTHx1O7dm0g5UuYm5sb0dHR9OnTh169UiYEWrt2LdWqVePEiRPs3LmT559/nsuXL+Pj48OqVauIjo6mRo0arFy5kg4dOtCnTx+eeuopNm3alGGO1q1bIyJUqVIFf39/qlSpgoODA5UqVeLYsWMALF68mBo1alC9enX27t3Lr7/+ire3N25ubjz77LN8+eWXaUVgVFQUPXv2ZPbs2dy8edP2P8hUWpwppSxz7Ngx3n33Xfz8/PTszCzy8vKiTJky/Pzzz3z11VdWx1H53IQJE3BycqJ8+fJ8+umn7N+/n1GjRqX9TwcGBtKhQwcAnnzySXbv3g3AJ598Qvv27RERypYtS3BwMPv377/tuUeNGsWIESNYuHAhjzzyCB9//DHDhw/PMIerqysADg4Oabdv3U9KSuLo0aNMnjyZ9evXs3v3blq2bMn169dxcnJi69atdOjQga+++opmzZoB8MEHHzBmzBiOHz9OtWrVOH/+fPb+4O5C3wmVUpYwxvD6668DKW/cnp6eFifKfcLCwnB1dWX48OFcv37d6jhK3VW7du3YsGEDAN999x3lypUDoGTJkqxfvx6A06dP89tvvxESEpLW7uDBg5w4cYIGDRoQFxeHg4MDIvLAf++XL1/Gw8MDHx8fTp8+zZo1awC4evUqly5dokWLFkybNo2dO3cCcPjwYWrVqsWoUaMoWrRotpwckRl6zJlSyhJr1qxhw4YNlCxZksDAQKvj5EpOTk5Ur16dzZs3M2LECKZMmWJ1JGUHSpQoka1FRIkSJR76OYYOHUq3bt2YOnUqnp6ezJkzB4DXX3+dnj17UqVKFYwxTJw4kaJFi6a1GzFiBGPHjgWgS5cutGvXjunTpzNq1KgHyhEeHk716tWpVKkSISEhREVFAXDlyhXatm3L9evXMcYwdepUAF555RUOHjyIMYbGjRsTHp4zQ7BKXhppOiIiwkRHR1sdQyl1H9euXUv7Jly1alV8fX2tjpSr/fDDD5w7d45169ZRoUIFq+OoHLZv3z4qVqxodQx1Hxn9nkRkuzEm4s51tVtTKZXj3nnnHU6ePEmxYsUoUqSI1XFyvRo1agDoyQFK5RFanCmlctS+ffuYPXs2AQEBOqZZNnF3d6dChQocOHCAefPmWR1HKfWQ9F1RKZVjbk3h4uzsTGBgoI5plo3KlSuHu7s7Y8eO5dq1a1bHUTksLx2ilBdl9fejxZlSKsesXLmSzZs3ExAQkC0HGav/5+DgQPXq1bl27RrDhg2zOo7KQW5ubpw/f14LNDtljOH8+fO4ublluo2eEKCUyhHx8fE0bNiQK1euEB4eftsZWSr7/PDDD5w/f56NGzdSpkwZq+OoHJCYmEhMTIwOp2LH3NzcCAwMxNnZ+bbldzshQIfSUErliH/961/ExMRQoUIFChcubHWcPKt69ep88803DBw4kFWrVlkdR+UAZ2dngoODrY6hspF2ayqlbO7kyZO8//77+Pr6UqpUKT0JwIY8PDwICQlh586drF271uo4SqkHYNN3SBFpJiK/icghERmaweNtRWS3iOwUkWgRqZvZtkqp3GP8+PHcuHGD4sWL4+HhYXWcPC8sLAxnZ2eGDRumxyEplQvZrDgTEUdgBtAcCAO6iEjYHautB8KNMdWAXsCcLLRVSuUCO3bsYOnSpQQEBBAUFGR1nHzB2dmZypUrc/r0aaZPn251HKVUFtlyz1kkcMgYc8QYcwNYBLRNv4Ix5qr5/691HoDJbFullP0zxvDGG2/g7u5OYGAgLi4uVkfKN0qXLo2npyfvv/8+ly5dsjqOUioLbFmclQDST+4Vk7rsNiLypIjsB1aRsvcs021T2/dN7RKNPnv2bLYEV0plj2XLlrFjxw4CAgIoVqyY1XHyFRGhWrVqxMfH8+qrr1odRymVBbYsziSDZX85+MEYs8wYUwFoB4zOStvU9h8aYyKMMRE6P59S9iM+Pp5x48ZRsGBBSpYsqScBWMDPz4+AgABWrVrFgQMHrI6jlMokW75bxgDpDzAJBE7cbWVjzP+AMiJSNKttlVL2Z86cOZw8eZKAgAAKFixodZx8Kzw8HGMM//znP62OopTKJFsWZ9uAUBEJFhEXoDOwIv0KIlJWRCT1dg3ABTifmbZKKft1/vx53nvvPYoWLapDZ1jMw8OD4OBgduzYwffff291HKVUJtjsHdMYkwQ8D6wF9gGLjTF7RaSfiPRLXa0DsEdEdpJydmYnkyLDtrbKqpTKXlOnTiU+Pl6HzrATYWFhODk56bFnSuUSOn2TUipbHT58mMcee4yiRYvyyCOP4OrqanUkBfz222/s3buXyZMn06VLF6vjKKW4+/RN2teglMpWEyZMQEQoUaKEFmZ2pGzZsri6ujJ27FgSExOtjqOUugctzpRS2Wbbtm2sXr0af39/SpTIcPQbZRFHR0eqVKnChQsXmDp1qtVxlFL3oMWZUipbGGMYPXo07u7uBAUF4eTkZHUkdYegoCC8vLz48MMPuXLlitVxlFJ3ocWZUipbrF69mu3bt+Pv74+/v7/VcVQGRITw8HDi4+MZMWKE1XGUUnehxZlS6qElJiYybtw4vL29CQoK0qEz7Jifnx++vr589dVXHD9+/P4NlFI5Tt9BlVIPbcGCBRw7dgx/f38KFy5sdRx1H+Hh4dy8eZMhQ4ZYHUUplQEtzpRSDyUuLo6pU6dSqFAhnaYpl/D29iYwMJDvv/+evXt1CEml7I2+iyqlHsrs2bM5e/YsAQEB+Pj4WB1HZVLlypUBeOWVVyxOopS6kxZnSqkH9ueffzJz5kyKFi1KyZIlrY6jssDd3Z3g4GB27dql0zopZWe0OFNKPbD33nuPa9euERAQoNM05UJhYWE4OjoyfPhwq6MopdLR4kwp9UBiY2P55JNP8PPzIygoyOo46gG4uLhQrlw5jhw5wrJly6yOo5RKpcWZUuqBTJ48GWMMxYsXp0CBAlbHUQ8oNDQUFxcXRo8eTV6aa1mp3EyLM6VUlu3fv58vvvgCPz8/naYpl3NyciIsLIzTp08ze/Zsq+MopdDiTCn1ACZMmICzszPFixfHxcXF6jjqIZUuXZoCBQowbdo0nRRdKTugxZlSKku2bdvGunXr8Pf3p3jx4lbHUdnAwcGBypUrc+nSJSZNmmR1HKXyPS3OlFKZZoxh/PjxuLu7U6JECZ3cPA8JDAzEy8uLTz75hPj4eKvjKJWv2bQ4E5FmIvKbiBwSkaEZPN5NRHanXn4SkfB0jx0TkV9EZKeIRNsyp1IqczZu3MiWLVvw9/fHz8/P6jgqG4kIVapUIS4ujnHjxlkdR6l8zWbFmYg4AjOA5kAY0EVEwu5Y7SjQwBhTFRgNfHjH442MMdWMMRG2yqmUypzk5GQmTJiAj48P/v7+utcsDwoICKBgwYJ89tlnXL582eo4SuVbttxzFgkcMsYcMcbcABYBbdOvYIz5yRhzIfXuZiDQhnmUUg/h66+/Zu/evfj5+eHr62t1HGUj4eHhJCQkMHr0aKujKJVv2bI4KwEcT3c/JnXZ3fQG1qS7b4BvRGS7iPS9WyMR6Ssi0SISffbs2YcKrJTKWGJiIm+//Ta+vr4ULVoUZ2dnqyMpGylSpAhFihThiy++4MyZM1bHUSpfsmVxJhksy3CEQxFpREpx9mq6xVHGmBqkdIsOEJH6GbU1xnxojIkwxkTot3mlbGPRokUcO3YMPz8/ChcubHUcZWNVq1YlMTGRt956y+ooSuVLtizOYoD0c7oEAifuXElEqgJzgLbGmPO3lhtjTqRenwGWkdJNqpTKYfHx8UydOpXAwEC8vb1xdXW1OpKysUKFCuHv78/XX3/NsWPHrI6jVL5jy+JsGxAqIsEi4gJ0BlakX0FESgJfAn83xhxIt9xDRLxu3QaaAntsmFUpdReffPIJp0+fxs/Pj4IFC1odR+WQKlWqkJycrHvPlLKAzYozY0wS8DywFtgHLDbG7BWRfiLSL3W1kUARYOYdQ2b4Az+IyC5gK7DKGPMfW2VVSmXs0qVLvP/++5QtWxY3NzedQzMf8fb2plixYqxbt469e/daHUepfMWm58IbY1YDq+9Y9kG6288Cz2bQ7ggQfudypVTOmjVrFpcuXaJ69ep6EkA+dGvOzdGjR7No0SKr4yiVb+gMAUqpDJ05c4Y5c+YQGRmJl5eXzqGZD3l5eVGiRAm+//57Nm/ebHUcpfINLc6UUhmaPn06N27coHnz5jg46FtFfhUYGIiHh4eOe6ZUDtJ3XKXUX/z+++/8+9//JioqipCQEKvjKAs5OTnRtm1bdu7cyTfffGN1HKXyhUwVZyKyVERaiogWc0rlA5MnT8bR0ZEnnnhCp2lSNGnShEKFCjFu3DiSk5OtjqNUnpfZYmsW0BU4KCITRKSCDTMppSz066+/smzZMho0aEBQUND9G6g8z8XFhQ4dOnDw4EGWLl1qdRyl8rxMFWfGmP8aY7oBNYBjwDoR+UlEnhERPYVLqTxk4sSJuLu707RpUxwdHa2Oo+xE/fr18ff3Z9KkSSQlJVkdR6k8LdPdlCJSBOhJytAXPwPTSSnW1tkkmVIqx23dupX//ve/PP744/j7+1sdR9kRR0dHOnXqRGxsLHPnzrU6jlJ5WmaPOfsS+B5wB1obY9oYYz43xrwAeNoyoFIqZxhjGDduHIUKFaJx48Z6hqb6i8jISEqXLs27775LfHy81XGUyrMy++47xxgTZowZb4w5CSAirgDGmAibpVNK5Zj169ezbds2mjZtqpObqwyJCJ07d+b8+fPMmDHD6jhK5VmZLc7GZLBsU3YGUUpZ5+bNm4wfPx5/f3/q16+PiFgdSdmpKlWqEBYWxuzZs7lw4YLVcZTKk+5ZnIlIgIg8AhQQkeoiUiP10pCULk6lVB7w5Zdfsn//flq0aIGPj4/VcZSd69q1K1evXmXy5MlWR1EqT7rfAEZPkHISQCDwTrrlV4DhNsqklMpB169fZ9KkSQQHB1O7dm3da6buKzg4mMjISBYsWMBzzz1HiRIlrI6kVJ5yzz1nxph5xphGQE9jTKN0lzbGmC9zKKNSyobmz59PbGwsLVu2xMPDw+o4Kpfo1KkTSUlJjBmT0VEvSqmHcb9uzadTb5YWkZfvvORAPqWUDV2+fJnp06dTqVIlatSooXvNVKYFBATQqFEjVq5cyf79+62Oo1Secr8TAm59jfYEvDK4KKVysVmzZnHx4kVatWqFq6ur1XFULtO+fXucnZ0ZNWqU1VGUylPuecyZMeZfqddv5UwcpVROOX36NB9++CE1a9akYsWKVsdRuVDBggVp3rw5X331FZs2baJOnTpWR1IqT8jsILRvi4i3iDiLyHoROZeuy/Ne7ZqJyG8ickhEhmbweDcR2Z16+UlEwjPbVin1cN555x0SExNp0aIFzs46C5t6MC1btsTT05NRo0ZhjLE6jlJ5QmbHOWtqjLkMtAJigHLAK/dqICKOwAygORAGdBGRsDtWOwo0MMZUBUYDH2ahrVLqAR0+fJiFCxdSt25dQkJCrI6jcjF3d3eefPJJdu/ezerVq62Oo1SekNni7NbX6hbAQmPMn5loEwkcMsYcMcbcABYBbdOvYIz5yRhzaxTDzaQM2ZGptkqpBzdhwgScnZ1p3rw5Tk73G1FHqXtr3LgxRYsWZdy4cTopulLZILPF2dcish+IANaLiC9w/T5tSgDH092PSV12N72BNVltKyJ9RSRaRKLPnj17n0hKqW3btrF69Woef/xxHZ9KZQtnZ2c6derEsWPHmD9/vtVxlMr1MlWcGWOGAnWACGNMInCN++/Jyuic/AwPSBCRRqQUZ69mta0x5kNjTIQxJsLX1/c+kZTK34wxjB49mkKFCtGkSROd3Fxlmzp16lC6dGmmTp3KtWvXrI6jVK6WlXfmikAnEekOPAU0vc/6MUBQuvuBwIk7VxKRqsAcoK0x5nxW2iqlsmbVqlVs376d5s2bU6RIEavjqDxERHj66af5888/mTp1qtVxlMrVMnu25qfAZKAuUDP1EnGfZtuAUBEJFhEXoDOw4o7nLQl8CfzdGHMgK22VUllz48YNxo0bR2BgoE5urmyiYsWKVKtWjU8++YRTp05ZHUepXCuze84igChjzHPGmBdSLwPv1cAYkwQ8D6wF9gGLjTF7RaSfiPRLXW0kUASYKSI7RST6Xm2zvHVKqTTz58/n999/p3Xr1nh6elodR+VR3bp148aNGzqtk1IPIbOnae0BAoCTWXlyY8xqYPUdyz5Id/tZ4NnMtlVKPZhLly4xdepUwsLCeOSRR3SvmbKZ4sWL07BhQ5YvX86AAQN0gGOlHkBm95wVBX4VkbUisuLWxZbBlFLZ5/333+fSpUu0adOGAgUKWB1H5XFPPfUUzs7OjBw50uooSuVKmd1z9qYtQyilbCcmJoY5c+ZQq1YtKlSoYHUclQ/4+PjQqlUrli5dyrfffkvDhg2tjqRUrpLZoTS+A44Bzqm3twE7bJhLKZVNJk6ciDGGli1b6jRNKse0bNkSHx8f3njjDZKTk62Oo1SuktmzNfsAS4B/pS4qAXxlo0xKqWyyfft2vvzySx577DFKlSpldRyVj7i6utKpUycOHTqkA9MqlUWZPeZsABAFXAYwxhwE/GwVSin18JKTk3njjTcoVKgQzZo1w9HR0epIKp+pV68epUqVYvLkyVy9etXqOErlGpktzhJS57gEQEScuMuI/Uop+/DVV1/x888/07JlS3T2DGUFBwcHevTowYULF3j77betjqNUrpHZ4uw7ERkOFBCRJsAXwNe2i6WUehhxcXGMHTuW4OBg6tWrp0NnKMuUL1+eyMhI5s+fz7Fjx6yOo1SukNnibChwFvgF+Acp44+9ZqtQSqmHM2vWLE6dOkW7du3w8PCwOo7K57p27QrAa6/px4ZSmZHZszWTSTkB4DljzFPGmNnGGO3WVMoOxcbGMnPmTGrWrEnVqlV1r5mynK+vL82bN2fjxo18//33VsdRyu7dsziTFG+KyDlgP/CbiJwVER1ZUCk7NX78eJKTk2nTpg0uLi5Wx1EKgLZt2+Lj48Prr7+uQ2sodR/323P2EilnadY0xhQxxhQGagFRIjLI1uGUUlkTHR3NsmXLaNy4sQ6doeyKm5sbnTt35uDBgzq0hlL3cb/irDvQxRhz9NYCY8wR4OnUx5RSdiI5OZmRI0dSqFAhmjZtqkNnKLtTt25dSpcuzaRJk7h8+bLVcZSyW/crzpyNMefuXGiMOQvoUONK2ZGFCxeya9cu2rRpo0NnKLvk4OBAz549uXjxIqNHj7Y6jlJ2637F2Y0HfEwplYP+/PNPxo0bR/ny5albt66eBKDsVmhoKPXr12fRokXs2bPH6jhK2aX7FWfhInI5g8sVoEpOBFRK3d+ECRO4cuUKTz31FO7u7lbHUeqeunTpgqurK6+88gp64r9Sf3XP4swY42iM8c7g4mWMuW+3pog0E5HfROSQiAzN4PEKIrJJRBJEZPAdjx0TkV9EZKeIRGd905TKH3bu3MmCBQto2LAh5cqVszqOUvfl7e1Nx44d2b17NwsWLLA6jlJ2J7OD0GaZiDgCM4DmQBjQRUTC7ljtT2AgMPkuT9PIGFPNGBNhq5xK5WbJyckMHz6cggUL0qJFC5ycnKyOpFSmPP7445QsWZLx48fryQFK3cFmxRkQCRwyxhxJnZdzEdA2/QrGmDPGmG1Aog1zKJVnpT8JwN/f3+o4SmWag4MDvXr14sKFC3pygFJ3sGVxVgI4nu5+TOqyzDLANyKyXUT6ZmsypfIAPQlA5XZ6coBSGbNlcZbRJ0VWjvyMMsbUIKVbdICI1M/wRUT6iki0iESfPXv2QXIqlSvpSQAqL9CTA5T6K1sWZzFAULr7gcCJzDY2xpxIvT4DLCOlmzSj9T40xkQYYyJ0bCeVX2zdupXPPvtMTwJQuZ63tzedOnVi9+7dzJs3z+o4StkFWxZn24BQEQkWERegM7AiMw1FxENEvG7dBpoCus9bKSAhIYEhQ4ZQtGhRWrVqpScBqFyvcePGlClThvHjx3PmzBmr4yhlOZsVZ8aYJOB5YC2wD1hsjNkrIv1EpB+AiASISAzwMvCaiMSIiDfgD/wgIruArcAqY8x/bJVVqdxk5syZHDx4kL/97W86E4DKExwcHOjbty/x8fEMGTLE6jhKWc6mX7mNMauB1Xcs+yDd7VOkdHfe6TIQbstsSuVGhw4d4t133yUyMpKaNWvqSQAqzwgMDKRVq1YsX76cNWvW0Lx5c6sjKWUZW3ZrKqWyUXJyMkOGDMHFxYX27dvj6upqdSSlslW7du3w9/dn2LBhXLt2zeo4SllGizOlcomFCxeyZcsW2rZtS4kSWRmVRqncwcXFhT59+nD27Fneeustq+MoZRktzpTKBU6fPs2YMWOoUKECDRs2xMFB/3VV3lSxYkUaNGjAggULiI7WmftU/qTv8ErlAiNHjiQ+Pp6//e1vOqaZyvO6deuGl5cXL7/8MomJOoGMyn+0OFPKzn399desXLmSZs2aERoaanUcpWzOw8ODnj17cvjwYSZPvtvUy0rlXVqcKWXHzp49y7BhwwgJCaFFixY4OjpaHUmpHFGrVi1q1qzJrFmz2Llzp9VxlMpRWpwpZaeMMQwZMoSrV6/StWtXvLy8rI6kVI7q3bs3Hh4ePP/88yQkJFgdR6kco8WZUnZqyZIlfPPNN7Rq1Ypy5crpmGYq3/Hy8qJ3794cPXqUsWPHWh1HqRyjxZlSdujEiROMHDmScuXK0axZM+3OVPlWREQEUVFRfPLJJ2zZssXqOErlCC3OlLIzxhgGDx7MjRs36Nq1K56enlZHUspSPXr0wMfHh4EDBxIXF2d1HKVsToszpezMv//9b7777jvatm1LmTJlrI6jlOU8PDzo27cvMTExvPnmm1bHUcrmtDhTyo4cOXKEUaNGUalSJR5//HEdbFapVFWrVqVRo0YsWLCAjRs3Wh1HKZvSd36l7ERCQgLPPfccDg4OdOnSRQebVeoOTz/9NL6+vrzwwgucO3fO6jhK2YwWZ0rZifHjx/PLL7/QtWtXSpUqZXUcpeyOm5sbAwcO5MqVK/Tr1w9jjNWRlLIJLc6UsgP//e9/mT17Ng0bNqROnTrananUXQQHB9O5c2c2bdrEe++9Z3UcpWxCPwGUstipU6cYNGgQpUqV4qmnnsLFxcXqSErZtWbNmhEeHs6UKVP4+eefrY6jVLazaXEmIs1E5DcROSQiQzN4vIKIbBKRBBEZnJW2SuUFN2/e5IUXXiAuLo7u3btTsGBBqyMpZfdEhP79++Pp6Unfvn25cuWK1ZGUylY2K85ExBGYATQHwoAuIhJ2x2p/AgOByQ/QVqlc77333uOnn36iQ4cOOguAUlng5eXFgAEDOHnyJIMGDbI6jlLZypZ7ziKBQ8aYI8aYG8AioG36FYwxZ4wx24DErLZVKrfbtGkT77zzDrVq1eKxxx7T48yUyqKwsDDatm3LmjVrmDt3rtVxlMo2tvw0KAEcT3c/JnVZtrYVkb4iEi0i0WfPnn2goErltNjYWP7xj3/g7+9Pp06dcHNzszqSUrlS+/btqVChAm+++Sbbt2+3Oo5S2cKWxVlG/TOZPe85022NMR8aYyKMMRG+vr6ZDqeUVa5fv06fPn2Ij4+nV69e+Pn5WR1JqVzL0dGRl156CS8vL3r16oV+SVd5gS2LsxggKN39QOBEDrRVym4ZYxg2bBi7du3i6aefpnz58nqcmVIPycvLi0GDBnHp0iV69OhBYuKdR8oolbvYsjjbBoSKSLCIuACdgRU50FYpuzVv3jwWL15My5YtefTRR/U4M6WySUhICL169WLXrl0MGzbM6jhKPRQnWz2xMSZJRJ4H1gKOwMfGmL0i0i/18Q9EJACIBryBZBF5CQgzxlzOqK2tsiqVE7Zu3cobb7xBeHg4bdq0wdnZ2epISuUp9evX5+jRoyxcuJBq1arx9NNPWx1JqQdis+IMwBizGlh9x7IP0t0+RUqXZabaKpVbnThxgr59++Ln50f37t3x9PS0OpJSeVK3bt04duwYr732GmFhYdSoUcPqSEplmfapKGVjV65coXv37ly7do1nnnkGf39/qyMplWc5OTnx0ksv4enpSffu3fnjjz+sjqRUlmlxppQNJSYm0rdvXw4cOMAzzzxDhQoV9AQApWzMx8eHV199levXr9OpUycuXrxodSSlskSLM6VsxBjDkCFD+N///keXLl2IjIzUEwCUyiFBQUG89NJLxMbG8vTTT5OQkGB1JKUyTT8plLKRqVOnpp2Z2bhxY5ycbHqIp1LqDpUrV6ZPnz78/PPPDBgwAGMyO9SmUtbS4kwpG/j888+ZMmUKjz76KO3atcPFxcXqSErlS/Xq1aNDhw6sWbOGt956y+o4SmWKfpVXKptt3LiRIUOGUKlSJZ5++mnc3d2tjqRUvvbkk09y9uxZZs+eTYkSJejTp4/VkZS6Jy3OlMpGP/74I71796ZEiRL07t0bHx8fqyMple+JCM8++ywXL17krbfewt3dnW7dulkdS6m70m5NpbLJ1q1b6dGjB76+vgwYMEDnzFTKjjg6OjJo0CAqVKjAq6++yhdffGF1JKXuSoszpbLBjh07+Pvf/06hQoUYMGAAxYsX1yEzlLIzLi4uvPLKK5QtW5aXX36Z5cuXWx1JqQxpcabUQ/rll1/o1q0bHh4eDBgwgKCgIC3MlLJTrq6uDB06lNKlS/PCCy+wZs0aqyMp9RdanCn1EH799Ve6dOmCq6srAwYMoFSpUlqYKWXn3NzcGDZsGIGBgfTr149169ZZHUmp22hxptQDio6O5qmnnkJEeO655wgJCdHCTKlcwt3dneHDhxMQEMCzzz6rXZzKrmhxptQD+Pbbb+ncuTMFChRg4MCBhIaGamGmVC7j6enJ66+/TsmSJRkwYABz5861OpJSgBZnSmXZ8uXL6dmzJ35+frz44ouULVtWCzOlcilPT09GjBhBWFgYI0aMYOrUqTqTgLKcFmdKZcG8efMYMGAAISEhDBw4UA/+VyoPcHNzY8iQIURGRjJ58mRGjhypBZqylBZnSmWCMYYpU6YwfPhwqlatyoABAwgICNDCTKk8wsnJiRdeeIFGjRrx8ccf89xzz+lk6coyNp0hQESaAdMBR2COMWbCHY9L6uMtgDigpzFmR+pjx4ArwE0gyRgTYcusSt1NXFwcgwYNYuXKlURFRdGtWzcd+V+pPMjBwYHevXvj7e3N8uXLiY2N5aOPPsLX19fqaCqfsVlxJiKOwAygCRADbBORFcaYX9Ot1hwITb3UAmalXt/SyBhzzlYZlbqfmJgYevXqxb59+xg8eDDBwcFamCmVh4kIHTt2pEiRInz22We0aNGCjz/+mCpVqlgdTeUjtuzWjAQOGWOOGGNuAIuAtnes0xaYb1JsBgqKSDEbZlIq07Zu3UqLFi04fvw48+bNo1mzZjg46JEASuUHtWvXZsyYMQC0a9eOFStWWJxI5Se2/KQpARxPdz8mdVlm1zHANyKyXUT63u1FRKSviESLSPTZs2ezIbbK74wxfPrpp3Ts2BEfHx++/vprGjVqxPHjxylQoIDV8ZRSOaBAgQJ4enqyYsUKKleuTP/+/ZkwYQJJSUlWR1P5gC2Ls4yOlL7z9Jd7rRNljKlBStfnABGpn9GLGGM+NMZEGGMi9LgA9bAuXrxIv379GDp0KHXr1mXlypWULVuWa9euER8fj5OTTQ/TVErZCQcHB4wxODk5sXjxYrp06cJ7773H3/72N2JjY62Op/I4WxZnMUBQuvuBwInMrmOMuXV9BlhGSjepUjazdetWmjZtyn/+8x+GDx/O/Pnz044vu/VtWc/OVCr/MMaQmJiIq6srkydP5t1332Xv3r00adKElStXWh1P5WG2LM62AaEiEiwiLkBn4M5O+xVAd0lRG7hkjDkpIh4i4gUgIh5AU2CPDbOqfCwpKYkpU6bQoUMHnJ2dWb58OQMGDNDjy5RSt+nQoQPffPMNISEh/OMf/2Dw4MHExcVZHUvlQTb79DHGJAHPA2uBfcBiY8xeEeknIv1SV1sNHAEOAbOB51KX+wM/iMguYCuwyhjzH1tlVfnXgQMHaN++Pe+88w7t27dn7dq1VKtWzepYSik7Vbp0aZYtW8bzzz/PokWLeOKJJ9iyZYvVsVQeY9MDaIwxq0kpwNIv+yDdbQMMyKDdESDcltlU/nb9+nXeffddZs6ciYeHB++//z5PPvmk1bGUUrmAs7Mzw4YNo379+rz88su0b9+ebt26MXz4cAoWLGh1PJUHaL+Nynd+/PFHHn/8caZPn07r1q357rvvtDBTSmVZVFQUGzdu5B//+AeLFi2iYcOGLF++XKd+Ug9NizOVb5w6dYpBgwbRsWNHkpOTWbhwIe+99x5Fixa1OppSKpdyd3dn5MiRrF69mmLFivHcc8/RvXt3Dh06ZHU0lYtpcabyvKtXrzJp0iTq1q3LsmXLGDBgAOvXr6d+/QxHZ1FKqSyrXLkyK1eu5K233mLLli089thjDB06lDNnzlgdTeVCWpypPCsxMZG5c+fy6KOPMm3aNB5//HG+/fZbhg8froPJKqWynaOjI88++yw//fQTf//731m4cCFRUVG88847XLt2zep4KhfR4kzlOTdu3ODzzz+nUaNGjBgxgtDQUFauXMkHH3xA6dKlrY6nlMrjihYtytixY9mwYQMNGzZkypQpREVF8a9//YurV69aHU/lAlqcqTzj2rVrzJ49m0cffZSXX34ZNzc35s6dy5IlS6hevbrV8ZRS+UyZMmWYPXs2y5cvp2zZsowaNYpatWoxadIkzp8/b3U8Zce0OFO53pkzZ5gyZQqRkZG8+eablCpVik8//ZR169bRpEkTHdVfKWWpiIgIlixZwooVK6hduzbTpk0jMjKSkSNHcuzYMavjKTukEwWqXCk5OZkffviBTz/9lG+++YakpCSaNGnCgAEDqFmzptXxlFLqLx555BE++ugjDhw4wMyZM5k3bx4fffQR9erV4+mnn6Zp06a4uLhYHVPZAS3OVK5y8uRJli5dyoIFC/j9998pVKgQvXr1olu3bpQtW9bqeEopdV/lypVj2rRpvPrqqyxatIgFCxbwj3/8A19fXzp16sTf/vY3fT/L57Q4U3bvzJkzrFq1ihUrVrB161YA6tSpw5AhQ2jWrBlubm4WJ1RKqawrVqwYgwYNYuDAgXz77bf8+9//ZubMmbz//vuEhYXRpk0b2rRpQ6lSpayOqnKYFmfKLh09epSNGzeyZs0aNm/eTHJyMhUqVGDw4MG0bduWkJAQqyMqpVS2cHR0pHHjxjRu3JhTp07x9ddfs2LFCiZMmMCECRMIDw+nRYsWNGrUiLCwMD2ONh/Q4kzZhfj4eDZt2sTGjRvZsGFD2kGyZcqUYeDAgbRp04by5ctbG1IppWwsICCAPn360KdPH2JiYtIKtfHjxzN+/HgCAgJo2LAhjRo1ol69evj4+FgdWdmAFmfKEhcuXGDbtm1s2bKFLVu28Msvv5CUlISbmxuPPvoozz77LI0aNdJxyZRS+VZgYCD9+/enf//+nD59mm+//ZYNGzawevVqFi1ahIhQsWJFIiMjiYyMpFatWgQEBFgdW2UDLc6UzV2+fJm9e/eye/du9uzZw+7du9PmnXNxcSE8PJx+/fpRp04dateurceQKaXUHfz9/enUqROdOnUiKSmJHTt28OOPP7JlyxYWL17M3LlzAQgKCqJKlSpUrVo17bpw4cLWhldZpsWZyjZXrlzh0KFDHDx48LZL+nF8AgICqFq1Ku3bt6d27dqEh4drMaaUUlng5OSUtrcMICkpib1797Jlyxa2b9/Onj17WL16ddr6xYoVo1y5coSGhqZdly1bVos2O6bFmcoUYwwXL17k1KlTnDp1ihMnTvDHH39w/Phx/vjjD37//Xf+/PPPtPVdXFwICQmhcuXKdOzYkapVq1K5cmV8fX0t3AqllMp7nJycCA8PJzw8PG3ZpUuX2LNnD7/88gt79+7l4MGDfPbZZ8THx6et4+3tTcmSJW+7FCtWjOLFixMQEEDhwoVxcNCx6q1g0+JMRJoB0wFHYI4xZsIdj0vq4y2AOKCnMWZHZtqqh5OUlMTly5e5ePEily5d4uLFi2mXc+fOce7cOc6fP8+5c+c4e/Ysp06d4vr167c9h5OTE4GBgZQsWZIWLVpQsmRJypYtS9myZSlVqhROTlr7K6WUFXx8fIiKiiIqKiptWXJyMrGxsRw8eJBDhw6lfbE+cOAA69evJyEh4bbncHFxwd/fH19fX4oWLUrRokUpUqQIRYoUoXDhwvj4+FCwYMG0i7e3tw6im01s9ukpIo7ADKAJEANsE5EVxphf063WHAhNvdQCZgG1Mtk2VzHGkJycTHJyMjdv3ky7vnVJSkoiKSmJ5ORkEhMTSUpK+sv1jRs30i6JiYkkJCSQkJDA9evXb7uOi4sjPj6euLi42y5Xrlzh6tWrXL58+S+FVnoODg4ULlw47R8xPDycJ554goCAAAICAihWrBjFihUjICBACzCllMolHBwcCAoKIigoiMcee+y2x5KTkzlz5gwnT57k1KlTt12fO3eOmJgYdu3axblz57h58+ZdX8PV1RVPT0+8vLzw8vLCw8MDd3d3ChQogLu7e9ptNzc33NzccHV1Tbt2dXXF2dkZFxeXtNtOTk4ZXjs6OuLk5ISTkxMODg44Ojri6Oj4l9u5ddgRW36yRgKHjDFHAERkEdAWSF9gtQXmG2MMsFlECopIMaB0JtrmuE6dOvHbb79hjEkrtlKik1Z4pV9+a9mtS0649Qd/65/g1qVIkSKULl067Z/m1vWtbzw+Pj4UKlSIggULUqhQIRwdHXMkb25yq6DOj259Ocitb3Tqwdx6H8uvf/c59b5tDxwcHNK+gN9LcnLybT0tt3pfLly4wOXLl7l27VrajoArV65w7do1zp8/n7aT4NaOg4SEhLTPT1sSkbRC7Vaxdud1+sutZQUKFGDTpk02z3c3tizOSgDH092PIWXv2P3WKZHJtgCISF+gL0DJkiUfLvF91K5dm1KlSmX4S83ol53+DyL95c4K39nZGQcHB5ycnG77NuDs7Jx2cXJywsXF5S+XO7916IenbTg7O+Pq6vqX3f75RcGCBTl+/DhJSUlWR1E5zMfHJ9/+3d96j1X/71bPysOeTGCM4caNG7f1+iQkJJCYmHhbL9GtL4a3epESExNv63FKf52+R+rOnipjzG23b13fefvWfWdn52z6iT0YWxZnGVUJd5bJd1snM21TFhrzIfAhQEREhE3L8EGDBtny6ZUd8/DwoEWLFlbHsEx+3nalVPYTkbSdCt7e3lbHsTu2LM5igKB09wOBE5lcxyUTbZVSSiml8hxbniO7DQgVkWARcQE6AyvuWGcF0F1S1AYuGWNOZrKtUkoppVSeY7M9Z8aYJBF5HlhLynAYHxtj9opIv9THPwBWkzKMxiFShtJ45l5tbZVVKaWUUspeSE6cLZFTIiIiTHR0tNUxlFJKKaXuS0S2G2Mi7lyuQ/8qpZRSStkRLc6UUkoppeyIFmdKKaWUUnZEizOllFJKKTuSp04IEJGzwO82fpmiwDkbv4a9ys/bDvl7+/PztkP+3n7d9vwrP29/Tm17KWOM750L81RxlhNEJDqjMyvyg/y87ZC/tz8/bzvk7+3Xbc+f2w75e/ut3nbt1lRKKaWUsiNanCmllFJK2REtzrLuQ6sDWCg/bzvk7+3Pz9sO+Xv7ddvzr/y8/ZZuux5zppRSSillR3TPmVJKKaWUHdHiTCmllFLKjmhx9hBEZLCIGBEpanWWnCIio0Vkt4jsFJFvRKS41ZlyiohMEpH9qdu/TEQKWp0pJ4nI30Rkr4gki0i+OL1eRJqJyG8ickhEhlqdJyeJyMcickZE9lidJaeJSJCIbBSRfal/8y9anSmniIibiGwVkV2p2/6W1Zlymog4isjPIrLSqgxanD0gEQkCmgB/WJ0lh00yxlQ1xlQDVgIjLc6Tk9YBlY0xVYEDwDCL8+S0PUB74H9WB8kJIuIIzACaA2FAFxEJszZVjpoLNLM6hEWSgH8aYyoCtYEB+eh3nwA8ZowJB6oBzUSktrWRctyLwD4rA2hx9uCmAkOAfHVGhTHmcrq7HuSj7TfGfGOMSUq9uxkItDJPTjPG7DPG/GZ1jhwUCRwyxhwxxtwAFgFtLc6UY4wx/wP+tDqHFYwxJ40xO1JvXyHlg7qEtalyhklxNfWuc+ol37zPi0gg0BKYY2UOLc4egIi0AWKNMbuszmIFERkrIseBbuSvPWfp9QLWWB1C2VQJ4Hi6+zHkkw9o9f9EpDRQHdhicZQck9qttxM4A6wzxuSbbQemkbLjJdnKEE5Wvrg9E5H/AgEZPDQCGA40zdlEOede226MWW6MGQGMEJFhwPPAGzka0Ibut+2p64wgpdvjs5zMlhMys/35iGSwLN/sQVAgIp7AUuClO3oN8jRjzE2gWupxtctEpLIxJs8feygirYAzxpjtItLQyixanN2FMebxjJaLSBUgGNglIpDStbVDRCKNMadyMKLN3G3bM7AAWEUeKs7ut+0i0gNoBTQ2eXCQwCz87vODGCAo3f1A4IRFWVQOExFnUgqzz4wxX1qdxwrGmIsi8i0pxx7m+eIMiALaiEgLwA3wFpF/G2Oezukg2q2ZRcaYX4wxfsaY0saY0qS8gdfIK4XZ/YhIaLq7bYD9VmXJaSLSDHgVaGOMibM6j7K5bUCoiASLiAvQGVhhcSaVAyTlm/dHwD5jzDtW58lJIuJ760x0ESkAPE4+eZ83xgwzxgSmfrZ3BjZYUZiBFmcq6yaIyB4R2U1K126+OcUceB/wAtalDiXygdWBcpKIPCkiMUAdYJWIrLU6ky2lnvzxPLCWlAPCFxtj9lqbKueIyEJgE1BeRGJEpLfVmXJQFPB34LHU//WdqXtT8oNiwMbU9/htpBxzZtmQEvmVTt+klFJKKWVHdM+ZUkoppZQd0eJMKaWUUsqOaHGmlFJKKWVHtDhTSimllLIjWpwppZRSStkRLc6UUkoppeyIFmdKKaWUUnbk/wBSn0bdtK43aQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-4, 4, 100)\n",
    "y = stats.norm.pdf(x, 0, 1)\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(x, y, linestyle=\"solid\")\n",
    "plt.fill_between(x.clip(-3, +3), 0, y, alpha=0.5, label=\"~99.7% mass\", color=\"C2\")\n",
    "plt.fill_between(x.clip(-2, +2), 0, y, alpha=0.5, label=\"~95% mass\", color=\"C1\")\n",
    "plt.fill_between(x.clip(-1, +1), 0, y, alpha=0.5, label=\"~68% mass\", color=\"C0\")\n",
    "plt.ylabel(\"Density\")\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:31.385987Z",
     "start_time": "2023-09-01T17:14:31.382952Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% CI for Short Email:  (0.06436609374091676, 0.18563390625908324)\n"
     ]
    }
   ],
   "source": [
    "exp_se = short_email.sem()\n",
    "exp_mu = short_email.mean()\n",
    "ci = (exp_mu - 2 * exp_se, exp_mu + 2 * exp_se)\n",
    "print(\"95% CI for Short Email: \", ci)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:31.463518Z",
     "start_time": "2023-09-01T17:14:31.387519Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd46289cdd0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(exp_mu - 4*exp_se, exp_mu + 4*exp_se, 100)\n",
    "y = stats.norm.pdf(x, exp_mu, exp_se)\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(x, y, lw=3)\n",
    "plt.vlines(ci[1], ymin=0, ymax=4, ls=\"dotted\")\n",
    "plt.vlines(ci[0], ymin=0, ymax=4, ls=\"dotted\", label=\"95% CI\")\n",
    "plt.xlabel(\"Conversion\")\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:31.468696Z",
     "start_time": "2023-09-01T17:14:31.464968Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5758293035489004\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.04690870373460816, 0.20309129626539185)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "z = np.abs(stats.norm.ppf((1-.99)/2))\n",
    "print(z)\n",
    "ci = (exp_mu - z * exp_se, exp_mu + z * exp_se)\n",
    "ci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:31.473147Z",
     "start_time": "2023-09-01T17:14:31.470047Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.5758293035489004"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.ppf((1-.99)/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:31.553746Z",
     "start_time": "2023-09-01T17:14:31.474596Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd462983b50>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TJxIREQHAiRMnGDRokG46LD5N/z6vlJnfiQooEcmQ119/neSxjEFBQUyePNmZ7Tc3KliwIBMnTnTay5YtY8mSJS4mEklbaGgox44dUxF1CWstx44dy/BFIFmaiVxEcpfdu3cTGRnptHv27HnFpca5UYMGDWjbti3z5yfdlGHw4MH8/e9/p2jRoi4nE0mpdOnS7N+/X6eaLxMaGkrp0hm7ra+uwhORdElISKBZs2asX78eSDp1t3Tp0hxxqxZPOHPmDHfeeSd//PEHAE2aNGH27NkupxKRrNBVeCKSZXPnznWKp+RTdyqe/pI/f34mTJjgtJcuXconn3ziYiIR8SYVUCJyTbt372b8+PFOu0ePHjp1l4qGDRvSpk0bpz1o0CCOHj3qYiIR8RYVUCJyVYmJifTp08e56q5y5co899xzLqfyXUOHDqVkyZIAHD9+nCFDhricSES8QQWUiFzVBx98wA8//AAknbqbMmWKTt1dRYECBVJclffJJ5/w9ddfuxdIRLxCBZSIpOn48eOMGjXKaXfp0kWn7tKhYcOGNGvWzGkPHjzY6cETkZxBBZSIpGn8+PGcOHECSLr8uVevXu4G8iNDhw6lYMGCAOzZs4cZM2a4nEhEPEkFlIikasOGDc68RgCjRo0ib968LibyL8WKFaN///5Oe9q0afzvf/9zMZGIeJIKKBG5Qnx8PAMHDnTajRs35p577nExkX9q164dNWvWBOD8+fMMGTJEM0CL5BAqoETkCm+88QZbtmwBkmbovXQclKRfYGAg48aNIyAg6VD79ddf8+mnn7qcSkQ8QQWUiKRw8ODBFBNC9urVizJlyriYyL/VqFGDjh07Ou3hw4dz9uxZFxOJiCeogBKRFEaMGMG5c+cAqFSpEl26dHE5kf/r168fxYoVA+DQoUMppjkQEf+kAkpEHGvXrk1x+5GxY8dqzicPKFCgAMOGDXPac+fOZfv27S4mEpGsUgElIkDSzYIv/U/+kUceoV69ei4mylkefvhh5/eZkJDAiBEjNKBcxI+pgBIRABYsWOAMHA8LC2PQoEEuJ8pZjDGMGDEixYDyr776yuVUIpJZ1yygjDFzjTF/GmOiLllW2Bizwhiz4+L3Qt6NKSLedPr0aV566SWn3a1bNyIiIlxMlDNVqVIlxc2GR4wYwYULF1xMJCKZlZ4eqDeB+y5bNgD4ylpbCfjqYltE/NSUKVM4duwYABERETzzzDMuJ8q5+vXrR4ECBQDYvXs3b775pruBRCRTrllAWWvXAMcvW/wQMO/iz/OAhz0bS0Syy+7du5k7d67THjJkCGFhYS4mytmKFCmS4pY4kydPdopXEfEfmR0DVdxaexDg4vfrPRdJRLLTyJEjiYuLA6BOnTo8+OCDLifK+Z544gkqVKgAJJ0+vXTeLRHxD14fRG6M6WyM2WCM2XDkyBFvr05EMmD16tWsWLEC+GuQszHG5VQ5X0hICC+++KLTnj9/vjOAX0T8Q2YLqMPGmJIAF7//mdYTrbWzrbW1rLW1kieSExH3xcfHM3z4cKfdsmVLatSo4V6gXObuu++mQYMGACQmJjJs2DBNayDiRzJbQC0Bku9N0BFY7Jk4IpJdFixY4EzmmC9fPgYM0LUg2ckYw/DhwwkMDASSJjH98ssvXU4lIumVnmkMFgDrgL8ZY/YbYzoB44HGxpgdQOOLbRHxE2fPnmXSpElOu3v37lx/vYYyZrebbrqJ9u3bO+0xY8YQHx/vYiIRSa/0XIXX2lpb0lobbK0tba193Vp7zFp7l7W20sXvl1+lJyI+bNasWSSPSSxZsiRPP/20y4lyr969e3PdddcBsGPHDhYuXOhyIhFJD81ELpLLHDp0iFmzZjntfv36adoCFxUpUoRu3bo57YkTJzo3cxYR36UCSiSXmTRpEjExMUDSzNjNmjVzOZE8/fTTlChRAoAjR46kKHBFxDepgBLJRbZt25biFNGQIUOcQczinrCwMPr16+e0Z86cyeHDh11MJCLXogJKJBcZPXo0iYmJADRo0MC5jF7c17x5cypXrgxATExMikH+IuJ7VECJ5BLffvstK1euBJIuoR8yZIjLieRSgYGBKbbJpdNMiIjvUQElkgskJiYyevRop92iRQuqVKniYiJJTcOGDalfvz6QtM3GjBnjciIRSYsKKJFcYPHixfz6668AhIaG0rdvX5cTSVqGDBni3E7nyy+/ZN26dS4nEpHUqIASyeEuXLiQ4ma1Tz31FBERES4mkqupWrUqzZs3d9pjxozRLV5EfJAKKJEcbv78+ezduxeA8PDwFHMOiW/q06cPISEhAGzatInPP//c5UQicjkVUCI52Llz55gyZYrTfu655yhQoIB7gSRdSpcuTceOHZ32+PHjdYsXER+jAkokB5s9ezZHjx4FICIigscff9zdQJJuPXr0IH/+/ADs3LmTDz74wOVEInIpFVAiOdSxY8eYOXOm0+7Tpw+hoaEuJpKMKFy4MM8884zTnjhxojODvIi4TwWUSA41depU555qN910U4qByeIfOnfuTLFixYCkexi++eab7gYSEYcKKJEcaN++fbz11ltOe8CAAbplix/KmzcvvXr1ctr//ve/OXnypGt5ROQvKqBEcqAJEyYQFxcHQK1atbjnnntcTiSZ1bZtW8qXLw/AqVOnmDFjhruBRARQASWS42zZsoWPPvrIaQ8aNMiZmFH8T3BwcIobDb/++uscPHjQxUQiAiqgRHKcyMhIZ+LFu+++m9tvv93lRJJVTZs2pXr16gDExsammJpCRNyhAkokB1m/fj1ffvklkHTD4AEDBricSDwhICCAgQMHOu0FCxawe/duFxOJiAookRzCWsvYsWOd9iOPPELlypVdTCSeVL9+ferVqwdAQkICEydOdDmRSO6mAkokh1i5ciU//vgjAEFBQfTp08flROJJl/coLl68mKioKBcTieRuKqBEcoDExETGjx/vtNu1a0e5cuVcTCTecNttt3Hfffc57cjISBfTiORuWSqgjDHPG2P+a4yJMsYsMMZommMRFyxZsoQtW7YAEBYWRs+ePV1OJN7Sr18/AgKSDt0rV67k+++/dzmRSO6U6QLKGFMK6AHUstZWAwKBxzwVTETSJy4ujgkTJjjtTp06cf3117uYSLzpb3/7G82aNXPa48aNc666FJHsk9VTeEFAmDEmCMgL/JH1SCKSEQsWLGDPnj0AhIeH07VrV3cDide98MILhISEALBhwwZWrFjhciKR3CfTBZS19gAwEdgHHAROWWuXeyqYiFxbTExMijmBunbtSsGCBd0LJNmiTJkytG/f3mlHRkaSkJDgYiKR3Ccrp/AKAQ8BNwARQD5jTLtUntfZGLPBGLPhyJEjmU8qIleYO3cuhw8fBqB48eI8+eSTLieS7NKjRw/y5s0LwG+//cbHH3/sbiCRXCYrp/DuBv5nrT1irY0DFgH1Ln+StXa2tbaWtbZW8l3FRSTrTp48yfTp0512r169CAsLczGRZKeiRYvSuXNnpz1x4kQuXLjgYiKR3CUrBdQ+4A5jTF6TdKOtu4CtnoklItcyc+ZMTp06BUD58uVp3bq1y4kku3Xp0oVChQoBsG/fPt59912XE4nkHlkZA/UD8CHwE/Drxfea7aFcInIVhw8f5rXXXnPa/fr1Izg42MVE4oYCBQrw3HPPOe0pU6YQHR3tYiKR3CNLV+FZa4dZa2+21laz1ra31p73VDARSdvUqVOJjY0FoGrVqjRt2tTlROKWjh07UrJkSQCOHDmSorAWEe/RTOQifmbPnj3Mnz/faQ8YMMCZWFFyn9DQUF544QWnPWPGDI4fP+5iIpHcQUddET8zceJE4uPjAbjjjjto1KiRy4nEbS1atODGG28E4MyZM8yYMcPlRCI5nwooET/y3//+N8Xl6gMGDCDpGg7JzYKCgujXr5/TfuONNzh48KCLiURyPhVQIn4kMjLSuW1H48aNqV27tsuJxFc0adKEGjVqABAbG8vkyZNdTiSSs6mAEvETP/74I1999RUAxhj69+/vciLxJcYYBg4c6LQXLlzIrl27XEwkkrOpgBLxA9Zaxo4d67QfffRRKleu7GIi8UX169fnH//4BwAJCQm89NJLLicSyblUQIn4gRUrVrB+/XoAgoOD6dOnj8uJxFdd2gv16aef8vPPP7uYRiTnUgEl4uMSEhIYN26c0+7QoQNly5Z1MZH4spo1a9KkSROnPWbMGGfcnIh4jgooER/34Ycfsn37dgCuu+46evbs6XIi8XX9+/cnMDAQgO+++441a9a4nEgk51EBJeLDYmJimDBhgtN+5plnKFKkiIuJxB/ceOONKe6NOGbMGBITE11MJJLzqIAS8WHz5s1z5vMpWrQonTt3djmR+Ivnn3+e0NBQIGn+sMWLF7ucSCRnUQEl4qNOnTrFv//9b6f9/PPPky9fPhcTiT8pUaIETz/9tNN+6aWXuHDhgouJRHIWFVAiPmrGjBmcPHkSgPLly9OmTRt3A4nf6dq1K+Hh4QDs27ePd955x91AIjmICigRH3Tw4EFee+01p92vXz9CQkJcTCT+qECBAvTo0cNpT548mTNnzriYSCTnUAEl4oNefvllYmNjAahevTpNmzZ1OZH4q44dOxIREQHA8ePHmTVrlsuJRHIGFVAiPmbbtm0sXLjQaQ8aNIiAAO2qkjmhoaH07dvXab/66qscOnTIxUQiOYOOyiI+ZvTo0c4l5w0aNKB+/fouJxJ/16xZM+fWPzExMUyaNMnlRCL+TwWUiA/59ttvWblyJZB0c9ghQ4a4nEhygsDAwBT/lhYuXMi2bdtcTCTi/1RAifiIxMRERo0a5bRbtGhBlSpVXEwkOUnDhg2d3szExERGjx7tciIR/6YCSsRHLFq0iKioKODKcSsinjBkyBCMMQCsXLmSb7/91uVEIv5LBZSID4iJiSEyMtJpd+7c2blySsRTqlatSosWLZz2qFGjdIsXkUxSASXiA+bOncsff/wBQJEiRejatavLiSSn6tu3r3OLl6ioKD766COXE4n4pywVUMaYcGPMh8aY34wxW40xdT0VTCS3OH78eIpbtvTu3Zv8+fO7mEhysoiIiBS3eBk/fjwxMTEuJhLxT1ntgZoKfG6tvRm4Bdia9Ugiuculs0NXqFCBtm3bupxIcrpu3bpRpEgRAP744w/mzp3rciIR/5PpAsoYUwCoD7wOYK29YK096aFcIrnCzp07eeutt5z24MGDCQ4OdjGR5Ab58+end+/eTvuVV17hyJEjLiYS8T9Z6YGqABwB3jDGbDLGvGaMueJW8caYzsaYDcaYDdpBRVIaOXIk8fHxANx+++3ce++9LieS3KJt27bceOONAJw9e5YJEya4nEjEv2SlgAoC/g+Yaa29FTgHDLj8Sdba2dbaWtbaWsWKFcvC6kRylq+//pqvvvoKSJo0c8SIEc4l5iLeFhwczLBhw5z2ggUL+O9//+tiIhH/kpUCaj+w31r7w8X2hyQVVCJyDfHx8QwfPtxpt2rViurVq7sXSHKlO++8k4YNGwJJk2sOGzYMa627oUT8RKYLKGvtIeB3Y8zfLi66C9jikVQiOdzbb7/Njh07AMiXLx/9+/d3OZHkRsYYhg0bRmBgIADr1q3j888/dzmViH/I6lV4zwHzjTG/ADWBsVlOJJLDnThxgokTJzrtHj16cP3117uYSHKzm266iQ4dOjjtUaNGcf78eRcTifiHLBVQ1trNF8c31bDWPmytPeGpYCI51eTJkzl58iQAZcuW5amnnnI3kOR6vXv3Jjw8HIC9e/dqWgORdNBM5CLZaOfOncybN89pDxkyxJkVWsQthQsXTjGtwZQpUzStgcg1qIASyUYjRoxwpi244447eOCBB1xOJJKkQ4cOVKxYEUia1uCll15yOZGIb1MBJZJNli9fzsqVKwFNWyC+J7VpDX7++WcXE4n4NhVQItkgJiYmxX9OrVu3plq1ai4mErnSnXfeyZ133gmAtZbBgweTmJjocioR36QCSiQbzJw5k3379gEQHh7OwIEDXU4kkrqRI0cSEhICwKZNm1i4cKHLiUR8kwooES/bu3cv06ZNc9r9+/encOHCLiYSSdsNN9xA165dnfbYsWM5cUIXWItcTgWUiJcNGzbMmVenRo0atG3b1uVEIlfXvXt3SpcuDSTNWxYZGelyIhHfowJKxItWrFjBihUrnPaYMWOcWZ9FfFVYWBgjR4502u+8844GlItcRgWUiJfExsamGDjepk0b/u//dLtI8Q/33HOPBpSLXIUKKBEvmTlzJnv37gU0cFz8jzHmigHl7733nsupRHyHCigRL9izZ48Gjovfu3xA+ZgxYzh+/LiLiUR8hwooEQ+z1tK/f39iY2MBqF69ugaOi9/q3r07ZcqUAZIGlI8YMcLlRCK+QQWUiId9+OGHfPvttwAEBAQQGRmpgePit8LCwhgzZozT/vDDD1mzZo2LiUR8gwooEQ86duxYir/QO3XqxC233OJiIpGsu+uuu3jwwQed9oABA4iJiXExkYj7VECJeNDw4cOdSQdLly5N3759XU4k4hkjR46kYMGCQNLksJMnT3Y5kYi7VECJeMjXX3/NokWLnPa4cePIly+fi4lEPKdYsWIMHTrUac+aNYuoqCgXE4m4SwWUiAdER0czYMAAp/3www87c+iI5BSPPfYYdevWBSAhIYF+/fqRkJDgcioRd6iAEvGASZMm8fvvvwNJcz7pSiXJiYwxREZGkidPHgB+/vln5s6d63IqEXeogBLJop9//pk5c+Y47RdffJGiRYu6mEjEe2688UZ69uzptF966SX27dvnYiIRd6iAEsmC2NhYevXq5ZzG+Pvf/07Lli1dTiXiXc8++yw333wzkHT6unfv3rrNi+Q6KqBEsmDixIls374dgLx58/LSSy9hjHE5lYh3hYSEMGnSJGd+s3Xr1ulUnuQ6WS6gjDGBxphNxphPPRFIxF+sX7+eWbNmOe2hQ4dSvnx59wKJZKOaNWvSvXt3pz1u3Dh27tzpYiKR7OWJHqiewFYPvI+I34iOjqZXr15YawGoX78+7du3dzmVSPbq1asXVapUAf46nR0fH+9yKpHskaUCyhhTGmgCvOaZOCL+YcyYMezZsweA/PnzM3HiRJ26k1wnJCSEqVOnEhwcDMCmTZuYOXOmy6lEskdWe6CmAP2ANEcPGmM6G2M2GGM2HDlyJIurE1+xatUqVq1a5XaMVDVv3pzmzZt77f2/+eYb3nzzTac9cuRISpUq5bX1ifiyKlWq0Lt3b6c9adIktmzZ4rX1eXv/zgpfPi6K52W6gDLG/Av401q78WrPs9bOttbWstbWKlasWGZXJz6mUaNGNGrUyO0Y2e706dO88MILTvuee+6hRYsWLiYScV/Xrl259dZbAYiLi6Nnz55cuHDB5VTZL7ceF3OrrPRA/R140BizB1gI3GmMeccjqcTnHThwgAMHDrgdI1tZaxk4cKDzucPDw4mMjNSpO8n1goKCmDJlCqGhoQBs2bKFyMhIl1Nlv9x4XMzNMl1AWWsHWmtLW2vLA48BK6217TyWTHxaz549U0ymlxu8//77fPzxx0573LhxXH/99e4FEvEhFStWTHE7o1mzZuW601m58biYmwW5HUD8U48ePdyOkCZvZNuxYweDBw922q1bt+bBBx/0+HpE/FmnTp1Ys2YNK1euBJIKihUrVlC8eHGPrSO3HXvEd5nky7CzQ61ateyGDRuybX0inhAbG8u//vUvtm5Nmq2jYsWKfPbZZ+TNm9flZCK+5+jRozRu3Jg///wTgH/+85+8++67BARo3mbxP8aYjdbaWqk9pn/Rkil79+5l7969bsdIVVRUFFFRUR57v9GjRzvFU548eZg5c6aKJ5E0FC1alFdeecUZG/jNN98wY8YMj72/p/dvT/Ll46J4nnqgJFOSLyP+8MMPXU5yJU9m+/zzz+nUqZPTHjNmDI8//niW31ckp4uMjOSVV14BIDAwkEWLFlGrVqp/yGdIbjn2iG+4Wg+UxkBJplx6KX9OdeDAgRSf8/7776djx44uJhLxHy+88AJr165lw4YNJCQk0K1bN5YvX07BggXdjuY1ueG4KH/RKTzJlLp161K3bl23Y3hNbGwsXbp04eTJkwBEREQwYcIETVkgkk5BQUFMnz7dKZj279/Pc889R2JimvMu+72cflyUlFRASabs3Lkzx9441FrL4MGD2bRpE5B0+mH69OkUKlTI5WQi/qV06dJMmjTJaX/11Ve8/PLLLibyrpx8XJQrqYCSTBkwYECKOV9ykrfffpuFCxc67WHDhlGnTh0XE4n4r/vvv59u3bo57cmTJ/PFF1+4mMh7cvJxUa6kQeSSKevXrwegdu3aLie5UlayrV+/nhYtWhAXFwdAs2bNmDp1qk7diWRBQkIC7du3Z/Xq1QBcd911LF26lIoVK2b4vXLqsUd809UGkauAErno0KFD3H///c78NdWqVePjjz8mLCzM5WQi/u/EiRM88MAD7Nu3D4Abb7yRpUuXkj9/fpeTiaRN80CJx/3222/89ttvbsdI1fr1652/BNPr/PnzdO7c2SmeChUqxOuvv67iScRDChUqxGuvvebcL2/Xrl307Nkzw4PKM7N/ZxdfPi6K56kHSjLFl+c7yWg2ay0vvPAC7733HgABAQEsWLCAf/zjH17LKJJbffzxxynGRPXo0YP+/fun+/U56dgjvk/zQInHDRkyxO0IHjNlyhSneIKkz6biScQ7Hn74YX755RdeffVVAF555RXKlClDmzZtXE6WdTnpuCjXpgJKMqVmzZpuR/CI999/n4kTJzrtli1b0rlzZxcTieR8gwYNYseOHc5NhwcMGEDJkiVp1KiRy8myJqccFyV9NAZKMsWX70eVXmvWrKFv375Ou379+rz00ku64k7Ey4KCgpg1axbVq1cHkq7S69Kli98fU3LCcVHSTwWUZMrw4cMZPny42zEybcuWLTz99NPEx8cDULlyZWbPnk1wcLDLyURyh3z58jFv3jxKlSoFwLlz5+jQoQMHDhxwOVnm+ftxUTJGg8glU5L/yqpWrZrLSa50rWx//PEHTZs25dChQwCUKFGCTz75hIiIiGzLKCJJtm/fzkMPPcTp06cBuOmmm/j444/TvGeePx97xP9oHiiRi44dO0bz5s3Zvn07kDSh30cffUSVKlVcTiaSe61du5Y2bdo4E9jWqlWLd999l3z58rmcTHI7zQMlHrd582Y2b97sdoxUrVmzhjVr1lyx/MSJE7Rq1copnoKCgpgzZ46KJxGX1atXj8mTJzvtDRs20LFjR2JiYq54blr7ty/w5eOieJ56oCRTfHm+k9SynTp1iscee4xffvkFSJrradq0aTz00EOuZBSRK73++uu8+OKLTrtBgwbMnTvXmXwT/O/YI/5N80CJx40ePdrtCOl29uxZ2rVr5xRPxhhefvllFU8iPqZTp06cP3+eMWPGALB69Wq6dOnCnDlzCAkJcTndtfnTcVGyTqfwJFNuvvlmbr75ZrdjXFN0dDQdOnTgp59+cpZFRkbSokULF1OJSFq6du1Knz59nPaXX35Jt27dnCtmfZm/HBfFM1RASab48v2okp05c4YOHTrwww8/OMtGjx5N27ZtXUwlItfSq1cvnnvuOae9bNkynn32Wc6fP+9iqmvzh+OieE6mT+EZY8oAbwElgERgtrV2qqeCiW+LjIwEfPdcf1xcHC1btnRO2wEMHTqUJ554wsVUIpIexhj69+/P+fPnmT17NpBURHXs2JGEhAQCAwNdTpg6Xz8uimdlehC5MaYkUNJa+5MxJj+wEXjYWrslrddoEHnOsXPnTgAqVqzocpIrrV27lueff579+/c7ywYPHkzXrl1dTCUiGWWtZfjw4bz22mvOssqVKxMZGcltt93mYrLU+fJxUTInW+aBMsYsBqZZa1ek9RwVUOJtO3bsoHXr1hw8eBBIutpu/PjxOm0n4qestUydOpUJEyY4yypVqsS7776ryW/F67w+D5QxpjxwK/BDKo91NsZsMMZsOHLkiCdWJz5g3bp1rFu3zu0YKWzevJlHHnnEKZ5CQkKYNWuWiicRP2aMoVevXowdO9a5T+WOHTt4+OGHnR4fX+GLx0Xxniz3QBljrgNWA2OstYuu9lz1QOUcvjbfyZIlS3j++eeJjY0Fknqe5s+fT/369V1OJiKesnjxYrp160by/1vh4eHMnDnTZ/ZzXzsuStZ57RSeMSYY+BT4wlr78rWerwIq59i7dy8A5cqVczVHYmIiEydOZOrUv65fCAoK4uabb+aLL75wMZmIeMPdd9/Ntm3bSExMBCAwMJBhw4bx5JNPOj1UbvGV46J4jlcm0jRJ/1JfB7amp3iSnMUXDhBnz56lR48eKQqlChUqUKBAAcLCwlxMJiLeEh4eTtWqVTly5AiHDh0iISGBF198ka1btzJmzBjy5MnjWjZfOC5K9snKGKi/A+2BO40xmy9+PeChXOLj3L4f1b59+3jooYdSFE8NGzbkk08+UfEkksNdd911LF26lFtvvdVZtmDBAlq1asXRo0ddy+X2cVGyV6YLKGvtt9ZaY62tYa2tefFrmSfDie965ZVXeOWVV1xZ97Jly7j//vv57bffnGVdunRh3rx5hIeHu5JJRLJXiRIl+PDDD2nWrJmzbP369dx777189913rmRy87go2U83E5ZMOXDgAAClSpXKtnXGxMQwbNgw5s+f7ywLCQkhMjKSli1buppNRLLH5fu3tZZXX32V0aNHO4PLjTF069aNPn36EBwc7Fo28X/ZMg9UeqiAksyKioqiW7duKS5bLlWqFDNnzvTJCfVEJHutWrWKHj16cPz4cWfZrbfeyrRp0yhfvrx7wcSveX0eKMl9Vq1axapVq7y+noSEBGbPnk3Tpk1TFE9NmzZlxYoVqRZPixcvZvHixV7PJiLZL639u1GjRnz55Zf885//dJZt2rSJe++9lw8++IDs6CzIruOi+Ab1QEmmZMd8J1u2bKFfv35s2rTJWRYWFsbo0aNp1apVmpcsay4WkZzrWvt3YmIir776KuPHjyc+Pt5Z3qBBA8aNG+fVK+V07Ml5vDKNgeRuM2bM8Np7x8TEMGXKFGbNmpXiAFi9enWmTZum+0yJSJoCAgJ49tlnqVevHl27dmXPnj0ArF69mjvvvJPevXvTuXNnr4yN8uZxUXyPTuFJplx//fVcf/31Hn/fNWvWcNdddzFt2jSneAoJCaF3794sXrxYxZOIpMstt9zC8uXL6dSpk9NbHRsby9ixY7n//vv56aefPL5Obx0XxTepgJJMWb58OcuXL/fY+23bto0OHTrQunVrZzZfgDvuuIMVK1bwwgsvuDpBnoj4n3z58jFy5Eg+/fRTqlSp4izfunUrTZs2pXv37uzbt89j6/P0cVF8mwooyZTZs2cze/bsLL/PwYMH6dOnD3fffTdfffWVs7xgwYJMnDiRDz74QL1OIpIlNWvW5LPPPmPo0KGEhoY6yz/66CMaNGjAiBEjUly9l1meOi6Kf9AgcsmU5INN4cKFM/362bNnM2fOHOcGwJA0f0vz5s0ZPHgwxYoVcyWbiPiurO7f+/btY8SIEXz++ecplhcoUIDu3bvTsWNHrrvuOleyie/RPFDiMw4cOMDs2bOZP38+MTExKR5r1KgRgwYNStHVLiLiDevXr2fUqFFs3LgxxfLw8HAef/xxnnzySYoUKeJSOvEVKqDE45YtS7przwMPpO/2hzt37mTGjBksWrSIuLi4FI9Vq1aNwYMHU79+fY9ke++99wBo1aqVR95PRHyHJ/dvay2fffYZ48aNY/fu3SkeCw0NpU2bNnTp0oXSpUun6/0yelwU36cCSjwuPfOdXLhwgeXLl/POO+/wzTffXPF45cqVee6552jatCkBAZ4bjqe5WERyLm/s33Fxcbz//vvMmDHDmfYgWWBgIHfffTft2rWjQYMGBAYGZms2cZfmgRKPmzt3bpqP7d27l3fffZf33nuPI0eOXPH47bffTvfu3WnUqFGak2GKiGSX4OBg2rZty2OPPcbSpUuZPn06UVFRQNLdEL744gu++OILSpcuTevWrXnssccoUaLEFe9zteOi5DwqoCRTChQokKJ9+PBhli5dypIlS1i/fv0VzzfGcPfdd9OtWzdq166dXTFFRNItMDCQBx98kKZNm7JmzRqmT5/Od9995zy+f/9+JkyYwMsvv0y9evV48MEHuf/++ylUqBBw5XFRcjYVUJIpixcv5tSpUwAsWbKE77//PtV7TZUoUYLHHnuMNm3a6A7lIuIXjDE0aNCABg0asHPnTt59913ef/99Tpw4AST1Sn3zzTd88803DBw4kPr169O0aVPi4+PJly8fDz30kMufQLKDCihJt7i4ODZs2MCqVat44403iI6OTvV5AQEBNGzYkHbt2nHXXXcRFKR/ZiLinypWrMiLL75Iv379+Oyzz5g/fz7r1q1zHo+Pj2flypWsXLkSgOuuu46dO3fSqFEjbrnllquOmRL/pkHkkqYLFy7wyy+/8OOPP/LDDz/www8/cObMmVSfa4zhjjvu4MEHH+SBBx6gaNGi2Zz2L8nTI4SFhbmWQUS8wxf27wMHDjhDFi692fnlChUqRN26dalTpw633347VapU0R+UfkZX4ck1WWvZu3cvv/76K7/++is//fQTmzZtSjHJ5eWCg4OpU6cO9913H02aNKF48eLZmFhExH2///47n3zyCcuXL2fjxo0kJiam+dx8+fJRq1YtatasSY0aNahevToRERG6mMaHqYCSFE6cOMGOHTvYsWMH27dvZ8uWLURFRXH69OlrvrZUqVI0atSIsLAwKlWqRNu2bbMhcca8+eabADz++OOu5hARz/Pl/fvtt9/mt99+49y5c3z99depXoV8ucKFC1O9enUqV67MTTfdRKVKlahUqRL58+fPhsRyLSqgcpmEhAT+/PNP9u/fz969e/n999/Zu3cv+/btY/fu3enaqZOVK1fO6X6uU6cOFSpUcG63Ar4534kvZxORrPHl/fvSbImJiWzbto0ff/zRGQZx8ODBdL9XiRIlqFChAmXLlqVs2bKUK1eOMmXKUKZMGYoWLerRufMkbZoHKgdISEjg1KlTnDx5kmPHjnHs2DGOHj3qfB0+fJiDBw9y8OBB/vzzz6t2I6clPDzc6VauXr06tWvXTnWuE4AFCxZk9SOJiOQolx4XAwICqFy5MpUrV6Zjx45Ya9m/fz/r1693hkpERUWlOa700KFDHDp0iLVr117xWFBQEMWLF6dEiRKULFmS4sWLU7RoUeerSJEiFClShPDwcAoUKKBiy0uyVEAZY+4DpgKBwGvW2vEeSeWnEhMTOX/+PHFxcVy4cIHz589z4cIFYmNjOX/+vPM9JiaG6OjoFF8xMTGcPXuWM2fOON/PnDnjFE3pOb2WXqGhoVSsWJFKlSpRsWJF/va3v1G9enVKlSqV7nPxwcHBHssjIpITXO24aIxxepAeffRRIOn/jOSxp8nDKnbs2MHu3bu5cOFCmu8VHx/PgQMHOHDgwDUzGWMoWLAg4eHhFCxYkOuuu478+fM73/Ply0e+fPkICwsjb968zldoaKjzlSdPHkJDQwkJCSFPnjwEBwcTEhJCSEhIri7OMl1AGWMCgelAY2A/sN4Ys8Rau8VT4TJi3759jB8/Hmut85XcC3NpOzEx8Yp2QkKCszwhIcFpX/pzfHw88fHxJCQkOD/HxcWl+DkhIcGNj56qIkWKEBERQbly5ShXrpzTDVy+fHlKly6d5X/0ut+ciEhKGT0uBgQEcMMNN3DDDTekWB4fH8++ffvYu3evM/wiuf3HH39w8uTJdGey1nLy5MkMvSYjAgMDCQ4OJigoiKCgIEJCQggMDCQoKMj5HhQUREBAAIGBgQQGBqb42RjjLEv+MsZc8T2tr3HjxlGwYEGvfLZryUoPVB1gp7V2N4AxZiHwEOBKAXX69GkWL17sxqqzTcGCBSlYsKDTPXtpd23x4sUpWbIkJUqUoHjx4uTJk8erWT744ANABZSISDJPHReDgoKoUKECFSpUSPXxmJgY5xRf8rCNS4d1JA/zOHXqVJqnCD0luaPBLSNHjnRt3ZkeRG6MaQ7cZ6196mK7PXC7tbb7Zc/rDHQGKFu27G179+7NWuI0REVFce+993rlvdPLGJOiezM4ONjp+ry0GzRPnjwpukqTu04v7VZN/p7c9VqgQAFNyCYiIhkSHx/P6dOnOXHiBKdOneLs2bNXDBdJbVjJpcNOYmNjiY2N5cKFC85XXFwc58+fd/vj8csvv1CkSBGvvb+3BpGnNljmimrMWjsbmA1JV+FlYX1XVbp0aaZNm5ZmN19q3YHJ3YjJXYiXdiUmdy8mf13aHZn8PbnbMjg4mODgYOc9REREfEFQUBCFCxemcOHCHn9va+0VQ1ouXLiQYqhL8hCY5J6qy4fJXDq0Jvmx5I6d5OWXD71JXre1lnz58nn8c6VXVgqo/UCZS9qlgT+yFifzwsPDeeSRR9xavYiISK5ijHE6EHLjnR+yMpJ4PVDJGHODMSYEeAxY4plYIiIiIr4r0z1Q1tp4Y0x34AuSpjGYa639r8eSiYiIiPioLM0DZa1dBizzUBYRERERv5B7Z8ASERERySQVUCIiIiIZpAJKREREJINUQImIiIhkUKZnIs/Uyow5AnhiKvKiwFEPvI94h7aP79M28m3aPr5P28i3eWr7lLPWFkvtgWwtoDzFGLMhranVxX3aPr5P28i3afv4Pm0j35Yd20en8EREREQySAWUiIiISAb5awE12+0AclXaPr5P28i3afv4Pm0j3+b17eOXY6BERERE3OSvPVAiIiIirlEBJSIiIpJBPlVAGWPuM8ZsM8bsNMYMSOVxY4x55eLjvxhj/i+9rxXPyOI22mOM+dUYs9kYsyF7k+cO6dg+Nxtj1hljzhtj+mTkteIZWdxG2oe8LB3bp+3FY9svxpi1xphb0vta8YwsbiPP7UPWWp/4AgKBXUAFIAT4Gahy2XMeAD4DDHAH8EN6X6svd7fRxcf2AEXd/hw59Sud2+d6oDYwBuiTkdfqy91tdPEx7UPub596QKGLP9+v/4f8ZxtdbHtsH/KlHqg6wE5r7W5r7QVgIfDQZc95CHjLJvkeCDfGlEznayXrsrKNxPuuuX2stX9aa9cDcRl9rXhEVraReF96ts9aa+2Ji83vgdLpfa14RFa2kUf5UgFVCvj9kvb+i8vS85z0vFayLivbCMACy40xG40xnb2WMvfKyn6gfSh7ZPX3rH3IuzK6fTqR1OOemddK5mRlG4EH96GgrLzYw0wqyy6fYyGt56TntZJ1WdlGAH+31v5hjLkeWGGM+c1au8ajCXO3rOwH2oeyR1Z/z9qHvCvd28cY04ik/5z/kdHXSpZkZRuBB/chX+qB2g+UuaRdGvgjnc9Jz2sl67KyjbDWJn//E/iIpK5Y8Zys7Afah7JHln7P2oe8Ll3bxxhTA3gNeMhaeywjr5Usy8o28ug+5EsF1HqgkjHmBmNMCPAYsOSy5ywBOly80usO4JS19mA6XytZl+ltZIzJZ4zJD2CMyQfcA0RlZ/hcICv7gfah7JHp37P2oWxxze1jjCkLLALaW2u3Z+S14hGZ3kae3od85hSetTbeGNMd+IKkUfZzrbX/NcY8c/HxWcAykq7y2glEA09c7bUufIwcLSvbCCgOfGSMgaR/d+9aaz/P5o+Qo6Vn+xhjSgAbgAJAojGmF0lXsJzWPuR9WdlGQFG0D3lVOo9xLwJFgBkXt0W8tbaW/h/KHlnZRnj4/yHdykVEREQkg3zpFJ6IiIiIX1ABJSIiIpJBKqBEREREMkgFlIiIiEgGqYASERERySAVUCLiNcaYEsaYhcaYXcaYLcaYZcaYm9zOBWCMeTC1O7mLiKSHpjEQEa8wSZOtrAXmXZybBWNMTSC/tfabbMwRaK1NyK71iUjuoB4oEfGWRkBccvEEYK3dDHxrjJlgjIkyxvxqjGkFYIxpaIz52hjzoTHmN2PM/Isz2t9vjHk/+T0uPu+Tiz/fY4xZZ4z5yRjzgTHmuovL9xhjXjTGfAu0MMb0uNgD9osxZuHF5zxujJl28edyxpivLj7+1cWZjDHGvGmMecUYs9YYs9sY0zx7fnUi4ut8ZiZyEclxqgEbU1n+KFATuIWk2bXXG2OSb+Z5K1CVpHtbfQf8HVgBvGqMyWetPQe0At4zxhQFhgB3W2vPGWP6A72BkRffK9Za+w8AY8wfwA3W2vPGmPBUMk0D3rLWzjPGPAm8Ajx88bGSJN2M9GaSbhnxYSZ+FyKSw6gHSkSy2z+ABdbaBGvtYWA1UPviYz9aa/dbaxOBzUB5a2088DnQ1BgTBDQBFgN3kHSLk++MMZuBjkC5S9bz3iU//wLMN8a0A+JTyVQXePfiz2+T8u7tH1trE621W0i6FYSIiHqgRMRr/gukdsrLXOU15y/5OYG/jlHvAd2A48B6a+2Zi2OsVlhrW6fxXucu+bkJUB94EBhqjKl6jeyXDg69NNPVsotILqIeKBHxlpVAHmPM08kLjDG1gRNAK2NMoDGmGEmFzY/XeK+vgf8DnuavnqXvgb8bYypefO+8qV3hZ4wJAMpYa1cB/YBw4LrLnraWpLu6A7QFvk3nZxSRXEo9UCLiFdZaa4x5BJhycbqAWGAP0IukAuZnknp6+llrDxljbr7KeyUYYz4FHifpVB3W2iPGmMeBBcaYPBefOgTYftnLA4F3jDEFSepBmmytPXnxjuzJegBzjTF9gSPAE5n93CKSO2gaAxEREZEM0ik8ERERkQxSASUiIiKSQSqgRERERDJIBZSIiIhIBqmAEhEREckgFVAiIiIiGaQCSkRERCSD/h8vgmLhP14ABwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(exp_mu - 4*exp_se, exp_mu + 4*exp_se, 100)\n",
    "y = stats.norm.pdf(x, exp_mu, exp_se)\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(x, y, lw=3)\n",
    "plt.vlines(ci[1], ymin=0, ymax=4, ls=\"dotted\")\n",
    "plt.vlines(ci[0], ymin=0, ymax=4, ls=\"dotted\", label=\"99% CI\")\n",
    "\n",
    "\n",
    "ci_95 = (exp_mu - 1.96 * exp_se, exp_mu + 1.96 * exp_se)\n",
    "\n",
    "plt.vlines(ci_95[1], ymin=0, ymax=4, ls=\"dashed\")\n",
    "plt.vlines(ci_95[0], ymin=0, ymax=4, ls=\"dashed\", label=\"95% CI\")\n",
    "plt.xlabel(\"Conversion\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:31.559265Z",
     "start_time": "2023-09-01T17:14:31.555088Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% CI for Short Email: (0.06436609374091676, 0.18563390625908324)\n",
      "95% CI for Long Email: (0.01115382234126202, 0.09893792077800403)\n",
      "95% CI for No Email: (0.0006919679286838468, 0.08441441505003955)\n"
     ]
    }
   ],
   "source": [
    "def ci(y: pd.Series):\n",
    "    return (y.mean() - 2 * y.sem(), y.mean() + 2 * y.sem())\n",
    "\n",
    "print(\"95% CI for Short Email:\", ci(short_email))\n",
    "print(\"95% CI for Long Email:\", ci(long_email))\n",
    "print(\"95% CI for No Email:\", ci(no_email))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:31.653983Z",
     "start_time": "2023-09-01T17:14:31.560700Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd451a96810>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "\n",
    "x = np.linspace(-0.05, .25, 100)\n",
    "short_dist = stats.norm.pdf(x, short_email.mean(), short_email.sem())\n",
    "plt.plot(x, short_dist, lw=2, label=\"Short\", linestyle=linestyle[0])\n",
    "plt.fill_between(x.clip(ci(short_email)[0], ci(short_email)[1]), 0, short_dist, alpha=0.2, color=\"0.0\")\n",
    "\n",
    "long_dist = stats.norm.pdf(x, long_email.mean(), long_email.sem())\n",
    "plt.plot(x, long_dist, lw=2, label=\"Long\", linestyle=linestyle[1])\n",
    "plt.fill_between(x.clip(ci(long_email)[0], ci(long_email)[1]), 0, long_dist, alpha=0.2, color=\"0.4\")\n",
    "\n",
    "no_email_dist = stats.norm.pdf(x, no_email.mean(), no_email.sem())\n",
    "plt.plot(x, no_email_dist, lw=2, label=\"No email\", linestyle=linestyle[2])\n",
    "plt.fill_between(x.clip(ci(no_email)[0], ci(no_email)[1]), 0, no_email_dist, alpha=0.2, color=\"0.8\")\n",
    "\n",
    "plt.xlabel(\"Conversion\")\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hypothesis Testing\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:32.135826Z",
     "start_time": "2023-09-01T17:14:31.655540Z"
    },
    "tags": [
     "hide-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+vPrq1S2WUFVVxbRp0+jRo8dVlSOEuLYtWrQIk8nEzJkzjQ7FTinFHXfcwfr16yksLDQ6HCGuiiRnHmLu3Ln2SWhdxdfXlzlz5ri0DiFE66a1ZtGiRYwbN47o6Gijw7nAjBkzqKmpuaR1QghvI8mZEEIIh33//fdkZGR41FOzekOGDCEmJkam1BBeT5IzIYQQDluxYgUmk4lbb73V6FAuoZRiypQppKWlUV1dbXQ4QrSYJGdCCCEctnz5cm644QbD5za7nMmTJ1NcXMzXX39tdChCtJgkZ0IIIRxy7Ngxdu/ezbRp04wO5bLGjRuHxWIhJSXF6FCEaDFJzoQQQjhk5cqVAEydOtXgSC4vJCSEG2+8UZIz4dUkORNCCOGQ5cuX07t3b7p27Wp0KFc0YcIE9u7dy5kzZ4wORYgWkeRMCCFEkwoKCti4caNHN2nWq5+Q+6uvvjI2ECFaSJIzIYQQTVq1ahVWq9WjmzTrDR48mKCgIL788kujQxGiRSQ5u0YtX76cBx98kKlTp7J27Vqjw2kxb7oOb4pViIutWLGCmJgYBg8ebHQoTbJYLIwcOVKSM+G1JDlzkzfeeAOlFAcOHLBvS0pKIjMzk/LyckaPHn3F5ZvqVVRUMHToUPr370/v3r35zW9+0+Q58fHx9O3blwEDBjBkyBAApk2bxltvvcV7773HkiVLgNrlnUaNGkVNTU0Lr/LK1wlccq1z584lKiqKPn36OFS+1Wpl4MCB3HLLLS69jsbuycV1X87l7pGrYhXC1aqqqli7di233HILJpN3/NlITk5m37595OXlGR2KEM3mHb9lrcDu3bsZMGAAq1atAqCyspLc3Fzi4uJ45513mD59ukPLN/n5+fHFF1+wa9cudu7cSWpqKt9++22T523YsIGdO3eybdu2C7Y/99xzzJs3D6hd3mncuHH2xKElrnSdwCXXet9995Gamupw+X/5y19ISkq6ZLuzr6Oxe3K5ui/W1D1ydqxCuNqmTZsoLS1lypQpRofisNGjRwPS70x4J0nO3GTPnj08+eST9qRl3759JCUloZRi0aJFDvfjUErRpk0bAKqrq6murkYp1ex4tNb88pe/ZPLkyQwaNMi+fdq0aSxatKjZ5dW70nUCl1zrqFGjCAsLc6js7OxsVq1axQMPPODy67g4zsbqvpzL3SNXxSqEq6WmpmKxWBg7dqzRoThsyJAhBAYGStOm8Eo+RgfgbocOHbpkW7t27YiKisJms3HkyJFL9oeHhxMREUFNTQ1Hjx69YF+PHj0cqnf//v3cdtttPPvss5w7d449e/bQt29fqqqqyMjIID4+3uFrsFqtDB48mPT0dObNm8ewYcOueLxSiokTJ6KU4uGHH+ahhx5iwYIFrFu3jnPnzpGens4jjzwCQJ8+fdi6deslZdx4442UlJRcsv3ll19m/PjxTV4n0KJrbeixxx7jT3/60wVxNPc6HNFYnI3VfSWN3aPXXnvN6bEK4Q6rV6/mxhtvtH/o8AbS70x4s2suOTNCVlYW4eHhBAQEMGHCBNasWcPu3bvp168f+fn5hIaGXnD8+PHjOX369CXlPP/880ydOhWz2czOnTspKiri9ttvZ+/evVfss7V582aio6M5c+YMEyZMoGfPnsyfP5/58+dfcqzZbMbX15eSkhKCg4Pt2zdu3HhV1wk0eq2O+vzzz4mKimLw4MEXvNk29zqa+t42Fufl6r6Sxu5Rc2MVwhNkZWWxd+9eXnrpJaNDabbk5GSefvpp8vLyPHa5KSEa49LkTCk1CfgLYAb+qbV+8aL9PYF3gUHA/2mtX3b03Ja60pMuk8l0xf0+Pj4OPylraPfu3fanR1OmTGHRokWcOnWKadOmERAQQEVFxQXHr1u3zqFyQ0NDSU5OJjU19YrJWXR0NABRUVHcfvvtbNmyhVGjRl32+MrKSvz9/S/Y5siTsytdJ9DotTpq8+bNrFy5kpSUFCoqKiguLubuu+9m4cKFzboOR763F8fZkrrrOXqPGotVCE9Q3yd08uTJBkfSfA3nO7vjjjuMDUaIZnBZnzOllBn4GzAZ6AXMUkr1uuiws8B84OUWnOs1GjbtjR49mo0bN9oTmXbt2mG1Wh1OWvLy8igqKgJqRxSuW7eOnj172vePGzeOnJwc+9fnz5+3J1Xnz59n7dq1V0wSCgoKiIyMxGKxXLB948aN7Ny585JXwybNK10n0Kxrvfg6XnjhBbKzs8nMzGTx4sWMHTv2isnR5a7DERfH2VTdF8fa1D1yZqxCuNrq1avp1KkTvXp531uw9DsT3sqVAwKGAula6wytdRWwGLig17vW+ozWeitQ3dxzvUnDpMXPz4++ffvi6+trbzqbOHEimzZtcqisU6dOMWbMGPr168d1113HhAkT7FM72Gw20tPTL+hgn5uby8iRI+nfvz9Dhw7l5ptvZtKkSZctf8OGDS0ekdXUdcKl1zpr1ixGjBjBoUOHiI2N5e233270Oprraq6jsTgvp7FYr3SPXBGrEK5SVVXFunXrmDx5cosGHhnNYrFw/fXXO9QtQwiPorV2yQuYQW1zZP3X9wB/vcyxvwX+p4XnPgRsA7Z17txZX2z//v2XbPM0O3bs0HffffdVl7Nnzx79+OOPX1UZt99+uz548OBVx3I5jlyrJ1yHo/fE1bF6w8+v8G5VVVU6JydHHzx4UKenp+vi4mJts9m01lpv2LBBA/rTTz81Nsir8Lvf/U4rpXRRUZHRoQhxCWCbbiS3cWWfs8Y+Zmlnn6u1fhN4E2DIkCGOlu9RBg4cyJgxY7BarQ7NdXY5ffr04dVXX23x+VVVVUybNq1F/eoc5ci1esJ1OHpPPCFWIa7G73//e3Jzcy/Y1r9/f37yk5+wevVqLBYL48aNMyi6qzdy5Ei01nzzzTdXbDUQwpO4MjnLBjo1+DoWOOmGc73S3LlzjQ4BX19f5syZ4/J6XH2tzroOd9wTd33PhYDaDwNffvklO3bs4H//938xmUz2JveQkBCqq6s5ffo0ISEhQG1/s/Hjx3v1KOJhw4ZhNpvZtGmTJGfCa7gyOdsKJCqlEoAcYCYw2w3nCiGEaMBms7FlyxaWL19OYWEhSUlJlJaWEhISwtChQy84tr7faE5ODjabjU6dOrFq1SqmTJnilf3OgoKCGDRokMP9eoXwBC5LzrTWNUqpR4E11E6H8Y7Wep9S6pG6/a8rpTpQ218sBLAppR4Demmtixs711WxCiFEa1VcXMzf//53jh07RlxcHPfff79DzeipqakcPHiQuXPnsnLlSs6fP8+MGTO8Zm3NhkaOHMk//vEPqqqq8PX1NTocIZrk0nnOtNYpQMpF215v8P/T1DZZOnTuVcThlZ/4xLWttq+oEC1T31+yTZs2BAUFce+99zJ8+HCHk6vVq1fToUMHfvazn/HJJ5+wfv16LBYLt99+u4sjd76RI0fy5z//mR07djB8+HCjwxGiSd73EaiZ/P39KSgokD90wqtorSkoKJCJaUWzVVdXk5qayq9+9SvOnz+PyWTipz/9Kddff73DiVl1dTVpaWlMnjwZs9nMD3/4Q0aNGsX69evJz8938RU43w033AAgTZvCa7T65ZtiY2PJzs4mLy/P6FCEaBZ/f39iYxt9sCxEo3bv3s1HH31EXl4e/fv3p6qqiqCgoGaX880331BcXGxfFUApxcyZM0lOTiYiIsLZYbtc+/btSUxMZNOmTfzP//yP0eEI0aRWn5xZLBYSEhKMDkMIIVympqaG999/n++++46OHTsyf/58evfu3eLyVq9ejY+PzwUrgJjNZmJiYgDYtm0bPXr08KpRnCNHjmTlypXSzUV4hVbfrCmEEK2d2WzGarVyyy238Mwzz1xVYga1ydkNN9xgn1KjobNnz/Luu+/y3nvveVV3kZEjR1JQUMChQ4eMDkWIJklyJoQQXurQoUPk5eWhlOKBBx7g1ltvxcfn6hpETp48ya5duy670HlYWBgzZsxg7969XrUs0siRIwHpdya8gyRnQgjhhY4dO8Zf//pXli1bBuC0pro1a9YAXDY5A0hOTqZHjx4sXbqUs2fPOqVeV0tMTCQyMlKSM+EVJDkTQggvk5uby1//+ldCQkKYNWuWU8teu3YtHTp0sE9G2xilFPfccw82m42FCxd6RfOmUoqRI0dKcia8giRnQgjhRaqqqnj99drpIufPn99ov7CWstlsrFu3jvHjxzf5JC4yMpKZM2dy/fXXO61+Vxs5ciRHjx7l1KlTRocixBVJciaEEF4kNTWVkydPcv/999O+fXunlr1r1y7y8/OZMGGCQ8ffcMMNDBkyBKWUVzw9q+93tnnzZoMjEeLKJDkTQggvMmHCBObOnUufPn2cXnZaWhrABVNoOOKLL77g7bffdno8zjZw4EACAgK8aiCDuDZJciaEEF6guroaq9VKQEAAw4YNc0kdaWlp9O7dm+jo6GbHtnXrVnbt2uWSuJzFYrEwfPhw6XcmPJ4kZ0II4QVSUlJ4/vnnqaysdEn55eXlbNy40eEmzYbGjx9PdHQ0S5YsoaqqygXROc/IkSPZuXMnJSUlRocixGVJciaEEB4uNzeXtWvXEhMTg5+fn0vq2LRpE5WVlS1KzsxmM7Nnz6agoICUlBQXROc8I0eOxGaz8e233xodihCXJcmZEEJ4uE8//RSz2cyMGTNcVkdaWhoWi4XRo0e36PzExERGjBhBWloaxcXFTo7OeYYPH47JZJKmTeHRWv3amkII4c2OHj3K999/z6233krbtm1dVk9aWhrXX399ixZKrzd9+nRGjRrl1Ok9nC0kJIR+/fpJciY8mjw5E0IID7Zx40ZCQkKaPYKyOc6cOcPOnTtb1KTZUEhICF26dAFq+7B5qpEjR/Ltt99SXV1tdChCNEqSMyGE8GD33HMPTzzxBP7+/i6rY/369QBXnZzVS0tL4ze/+Y3HJmgjR46krKyM77//3uhQhGiUJGdCCOGBrFYrFRUVmM1mOnTo4NK60tLSaNeuHYMHD3ZKed27d6e4uJgVK1Y4pTxnGzVqFAD/+c9/DI5EiMZJciaEEB7o66+/5plnniE/P9+l9WitSUtLY+zYsZjNZqeUGRcXx+jRo/nyyy85ceKEU8p0po4dO9KjRw++/PJLo0MRolGSnAkhhIeprKzks88+IyoqivDwcJfWdejQIbKzs53WpFlv6tSptGnThg8++ACbzebUsp0hOTmZjRs3UlNTY3QoQlxCkjMhhPAw69ev59y5c0yfPr3JBcivVv2STc5OzgIDA7njjjvIzs7m5MmTTi3bGcaMGUNJSQk7duwwOhQhLiFTaQghhAcpKSlhzZo19O/fn27durm8vrS0NLp06WIfZelMw4YNo2fPnrRr187pZV+t+vncvvzyS4YOHWpwNEJcyKVPzpRSk5RSh5RS6UqpJxvZr5RSr9Xt362UGtRg3+NKqX1Kqb1KqQ+VUq4bqiSEEB5i27ZtVFZWcvvtt7u8rurqajZs2MDEiRNdUr7JZKJdu3ZorcnJyXFJHS3VoUMHevbsKf3OhEdyWXKmlDIDfwMmA72AWUqpXhcdNhlIrHs9BPyj7twYYD4wRGvdBzADM10VqxBCeIoxY8bwm9/8ho4dO7q8rm+//ZbS0lKnN2lebP369Tz33HMe17wp/c6Ep3Llk7OhQLrWOkNrXQUsBqZedMxU4H1d61sgVClV/47kAwQopXyAQMCzfquFEMLJzp07B+CWxAxqmzRNJhNjx451aT3Dhw/H39+fxYsXo7V2aV3NMWbMGEpLS9m+fbvRoQhxAVcmZzFAVoOvs+u2NXmM1joHeBk4AZwCzmmt1zZWiVLqIaXUNqXUtry8PKcFL4QQ7rR3716efvppjhw54rY609LSGDp0KKGhoS6tp02bNkybNo1Dhw55VCLUsN+ZEJ7EoeRMKbVUKXWzUqo5yVxjQ4wu/sjU6DFKqXbUPlVLAKKBIKXU3Y1VorV+U2s9RGs9JDIyshnhCSGEZ6ipqeGjjz4iLCyMhIQEt9RZWFjIli1bXN6kWe/GG2+kU6dOfPLJJ1RWVrqlzqa0b9+epKQkSc6Ex3E02foHMBs4opR6USnV04FzsoFODb6O5dKmycsdMx44prXO01pXA8uA6x2MVQghDFdZWUl+fj5ZWVmkp6dz6NAh9u/fj9VqBaC0tJRz585htVrZsGEDubm5/PCHP8THxz2D6Dds2IDNZnPZYICLmUwmZs6cidaa3Nxct9TpiDFjxrBp0yZZZ1N4FIeSM631Oq31XcAgIBNIU0p9rZS6XyllucxpW4FEpVSCUsqX2g79Ky86ZiUwp27U5nBqmy9PUducOVwpFahqJ/kZBxxo9tUJIYSL2Ww2zp8/T15eHsePH7d3Li8oKOD48ePk5+dTVVUFgK+vLyZT7dvumTNnSE9PZ+fOnRQXFzN06FD69u3rtrjXrl1LcHAww4YNc1ud3bp147nnnqNz585uq7MpycnJ0u9MeByHP6IppcKBu4F7gO+BRcBI4F4g+eLjtdY1SqlHgTXUjrZ8R2u9Tyn1SN3+14EUYAqQDpQB99ft+04p9QmwA6ipq+/Nll2iEEI4R/1TL7PZTElJCSdOnKCiosK+32w2ExkZiY+PDxEREYSFheHn59foRLLx8fFERERw+PBhoqOjiY+P59ixY25r1kxLSyM5ORmL5XKfr13DYrFgtVrZuXOn09byvBoN+50NHz7c4GiEqKUcGTmjlFoG9AT+DbxX93Srft82rfUQ14XouCFDhuht27YZHYYQohWw2WyUlpZSVlZmf1VWVhIfH094eDhlZWXk5OQQGBhof/n6+rZoRv+ioiLKy8vx9/e3zwsGuGx1gKNHj9KtWzcWLFjAo48+6pI6rmTjxo0sXLiQefPm0a9fP7fXf7HevXvTqVMnUlNTjQ5FXGOUUtsby6Ec7XP2T611L631C/WJmVLKD8BTEjMhhLhaNTU19s7qNTU1HDlyhJycHM6fP09AQADR0dEEBgYCtcsTJSYmEhMTQ7t27S77hOxytNb2RcFDQ0Pp2LGjfSb9M2fOcOzYMZetSemqJZscdf3119OxY0eWLFniEX29pN+Z8DSOJmfPNbLtG2cGIoQQRikvLyczM5Pdu3eTlVU7u4+vry/du3enf//+9O3bl65du9KxY0cCAgKcUue2bdt4/vnnOXDg0u60WmsKCws5cuSISyZITUtLo1OnTnTv3t3pZTvCbDbzwx/+kPz8fP7zn/8YEkNDycnJnD9/Hml5EZ7iismZUqqDUmowtZPBDlRKDap7JVM7MawQQnitmpoaTpw4wf79+yksLCQ8PJyYmP9OxxgcHOyS0ZNVVVUsXbqUTp060aNHj0v2d+jQgYSEBM6fP8+hQ4ec+kSnpqaGL774gokTJ7p8UfUr6dWrF0lJSaSkpFBeXm5YHACjRo0CZL4z4TmaenJ2E7WTwcYCrwKv1L1+Djzt2tCEEMK18vLyyMvLIzIykr59+xIXF+e0J2NXsmbNGgoLC5k5c6Z99ObFwsLCSExMpKqqisOHDzutiXPbtm0UFRUZ1qTZ0PTp04mIiKC4uNjQOKKioujdu7ckZ8JjXPEjodb6X8C/lFJ3aK2XuikmIYRwmZqaGqqqqggMDKR9+/aEhoa6JSGrV1BQwJo1a7juuuvo1q3bFY8NDg6mW7duVFRUXDaJa660tDSUUowbN84p5V2Nzp0789RTTxn6BK/emDFjeOedd6iurnb7CFYhLtZUs2b9rPzxSqmfX/xyQ3xCCOE0ZWVlHDhwgIyMDLTWmEwmtyZmANnZ2QQFBTF9+nSHjg8ODqZ+9ZOysrKrfoK2du1aBg0aRERExFWV4yxKKY+YZyw5OZmysjK2bt1qaBxCQNPznAXV/dvG1YEIIYQr1U8K6+PjQ5cuXQx7WtO/f3/69OmD2Wxu1nnV1dUcOnSIkJCQFsdfWFjIN998w5NPPtnsc10pJSWFDRs2EBsbS/v27Q2JoeF8Z9dfLwvSCGNd8cmZ1vqNun9/19jLPSEKIUTLaa3JyckhMzOToKAgkpKSCAoKavpEFzh69Cg2m63ZiRnUTt4aHR1NUVER2dnZLao/LS0Nq9XKlClTWnS+q0yaNAmLxcLy5csNiyEiIoK+fftKvzPhERxd+PxPSqkQpZRFKbVeKZV/uYXIhRDC05SVlREREUH37t0N60+Uk5PDn/70J7744osWl9G+fXuioqI4c+YMZ86cafb5KSkphIWFuXXJJkeEhIQwfvx4duzYYZ/KxAjJycls3rzZvtyWEEZxtIfpRK11MXALtYuVdwd+4bKohBDiKtlsNmpqalBK0bVrVzp37mxox/PVq1fj7+/PiBEjrqqc2NhY2rZtS1ZWFqWlpQ6fZ7PZSE1NZeLEiS16cudq48ePJyAggFWrVhkWg/Q7E57C0eSs/qPmFOBDrfVZF8UjhBBXzWq1cuTIEY4cOWLv+G9kYnb27Fm2b9/OyJEjr7pJVSlFQkICMTExzSrr+++/Jzc31+OaNOsFBgbaR5DWr2HqbjLfmfAUjiZnnymlDgJDgPVKqUigoolzhBDC7axWK+np6ZSWltK+fXuPmKZh/fr1AE6bvsJsNtOhQweUUlRXVzvUDLd69WoAbrrpJqfE4Aq33HILjzzyiGFP9iIiIujXr58kZ8JwDiVnWusngRHAEK11NXAemOrKwIQQorlsNhsZGRmUlpaSkJBAWFiY0SFhs9k4ePAggwcPdno8WmsOHz5Menp6k0+bUlJSuO6664iKinJqDM5Un0ifPn26RX3qnEH6nQlP0JxZDZOAO5VSc4AZwETXhCSEEC2Tk5NDcXExcXFxHpGYAZhMJp5++mlmzZrl9LKVUnTq1Iny8nL73G2NKSgo4Ntvv/XYJs2Gqqqq+OMf/8inn35qSP3JycmUl5ezZcsWQ+oXAhwfrflvapdxGglcV/ca4sK4hBCi2dq3b0/nzp09ZoJVrTVWqxWz2eyy6TtCQkLo3LkzxcXFlx3puHbtWrTWTJ482SUxOJOvry/Jycns2LGDnJwct9c/evRolFLStCkM5eiTsyHADVrrn2itf1r3mu/KwIQQwlHl5eVorfH19bXPpu8Jjh07xi9/+UuOHTvm0noiIyNp3749eXl5FBQUXLI/JSWFiIgIhgzxjs/U48ePx9/fn88//9ztdYeFhUm/M2E4R5OzvUAHVwYihBAtUV5ezsGDBzl58qTRoVxi06ZNVFVV0bFjR5fXFRMTQ8eOHWnbtu0F2+un0Ljppps8cgqNxgQFBTF27FjDnp4lJyfz9ddfU1lZ6fa6hQDHk7MIYL9Sao1SamX9y5WBCSFEU6xWKxkZGZhMJo96YgZQUVHBtm3bGDJkCP7+/i6vTylFdHQ0Pj4+2Gw2ysvLAdi2bRv5+fle0d+sofHjxxMcHMyJEyfcXrf0OxNGa2ptzXq/dWUQQgjREllZWVRUVJCYmIivr6/R4Vxg27ZtVFZWcsMNN7i97uPHj1NcXEyPHj1ISUlBKeXRU2g0JigoiBdeeMGQFR1GjRqFUooNGzZw4403ur1+IRydSuM/QCZgqfv/VmCHC+MSQogrKiwspKCggA4dOhASEmJ0OJfYtGkTHTt2pEuXLm6vu74Z9ciRI2zevJlhw4YRHh7u9jiuVn1i5u4m67CwMAYOHEhaWppb6xWinqOjNR8EPgHeqNsUAyx3UUxCCNEkHx8fQkND3dKfqyVuv/12ZsyYYcgkuP7+/nTr1o3q6mrmzp3Lbbfd5vYYnOWrr77i2WefdXvfs8mTJ/PNN99QVFTk1nqFAMf7nM0DbgCKAbTWRwDPnclQCNHqBQcH07VrV0ym5kzX6D49evSgT58+htUfFBREZmYmCQkJTJgwwbA4rtagQYPw8/Nz+5qbkyZNwmq1sm7dOrfWKwQ4npxVaq3t0yUrpXyAxmc7FEIIFyosLCQ7OxubzWZ0KI2qrq5m6dKlhs1w39Ann3zCH//4R3r16mV0KC3Wpk0bxowZw44dO9zavDl8+HBCQ0Pty14J4U6OJmf/UUo9DQQopSYAHwOfNXWSUmqSUuqQUipdKfVkI/uVUuq1uv27lVKDGuwLVUp9opQ6qJQ6oJQa4ehFCSFap5qaGk6cOEFJSYlHrJnZmF27drF27Vry8vIMjcNqtZKamkrbtm0JDAxEa01RUdFlVxHwZOPHj8fX19etT898fHyYMGECqampXvk9E97N0eTsSSAP2AM8DKQAz1zpBKWUGfgbMBnoBcxSSl388W0ykFj3egj4R4N9fwFStdY9gf7AAQdjFUK0UidPnqSmpobOnTt7bHK2adMmwsLCSEpKMjSO7777jsLCQvuqAMXFxRw9epScnByvSzbatGnD2LFjOXz4sH2KEHeYPHkyJ0+eZPfu3W6rUwhwcCoNrbVNKbUcWK61dvTj4FAgXWudAaCUWkztYun7GxwzFXhf175TfFv3tKwjtQurjwLuq6u/CpBVaIW4hpWWlpKXl0dUVJTLlkK6Wvn5+Rw4cIBbbrnF8L5wq1evxmQyMXFi7TLIISEhREZGkpubi9ls9tiBFJczadIkJk+ejJ+fn1vrhNrvZf/+/d1WrxBXfPeoa3b8rVIqHzgIHFJK5Smlfu1A2TFAw4Xesuu2OXJMF2qf1L2rlPpeKfVPpVSj78ZKqYeUUtuUUtuMbkYQQriG1pqsrCwsFgvR0dFGh3NZX3/9NUopQ+Y2u1hKSgojRoygXbt2wH8XSQ8LC+PkyZMe0SeuOfz9/fHz88NqtXL+/Hm31NmxY0cGDBhAamqqW+oTol5TH+0eo3aU5nVa63CtdRgwDLhBKfV4E+c21uZw8bP0yx3jAwwC/qG1Hkjtk7RL+qwBaK3f1FoP0VoP8bQZwoUQzqGUIj4+noSEBI9egshmszFw4EDCwsIMjeP06dPs2LHjklUB6r+Pbdu2JTs72+uWJ7LZbLz44ot8+OGHbqtz8uTJbN68meLiYrfVKURTydkcYJbW2r5qb10z5d11+64kG+jU4OtY4OKhNpc7JhvI1lp/V7f9E2qTNSHENaZ+VGZAQADBwcEGR3Nl06ZN46GHHjI6DPuTnsaWbFJK0aVLFxITE93aROgMJpOJXr16sW3bNk6dOuWWOidPnkxNTY1MSCvcqqnkzKK1zr94Y12/s6bW1NgKJCqlEpRSvsBM4OL1OFcCc+qaT4cD57TWp7TWp4EspVSPuuPGcWFfNSHENUBrzdGjRzl+/LjRoTQpLy8PrbVHDFRISUmhY8eOl+0nZTKZ7IluUVERZWVl7gzvqkyYMMGtIzdHjBhBWFgYK1ascEt9QkDTydmVOuFfsYO+1roGeBRYQ+1Iy4+01vuUUo8opR6pOywFyADSgbeAnzQo4qfAIqXUbmAA8IcmYhVCtDKFhYUUFxcTEBBgdChXVFxczK9//WvWrl1rdCjU1NSwdu1aJk+e3GSiaLPZyMrK4siRI17TxNmmTRuSk5PZtm0bp0+fdnl9Pj4+3HbbbXz22WdUVcm4NOEeTSVn/ZVSxY28SoC+TRWutU7RWnfXWnfVWj9ft+11rfXrdf/XWut5dfv7aq23NTh3Z11fsn5a62la68KruVAhhHepqakhKyuLwMBAPL0/6TfffIPNZvOIEX3ffPMN586ds0+hcSUmk4lu3bqhtSY9PR2r1eqGCK/ehAkTsFgsbN682S31TZ8+naKiIr788ku31CfEFZMzrbVZax3SyCtYa91Us6YQQrRYTk4ONTU1xMXFeURT4eVordm8eTNdu3alQ4cORodDSkoKZrPZ4SWbAgIC6NKlCxUVFWRmZnrFHGjBwcH87//+L7fffrtb6pswYQJBQUEsW7bMLfUJ4ZmL0gkhrmk1NTUUFhYSFRVFYGCg0eFc0aFDh8jNzeXGG280OhSgdk6ukSNH0rZtW4fPCQkJITY2lqKiIs6dO+fC6JynU6dOmEwmtzzt8/f35+abb2b58uVe83RReDdJzoQQHsfHx4fevXt79Jxm9b7++muCgoIYMmSI0aGQk5PDrl27HGrSvFhUVBSJiYnNSuqMtmfPHp5++mmKiopcXtf06dPJzc3l22+/dXldQkhyJoTwKGVlZWitsVgsHj2nWb27776b+fPnY7EY39PjSlNoNEUpRUhICEopysvLvWIEZ4cOHSguLmbdunUur2vKlCn4+vpK06ZwC0nOhBAeo6KigoMHD3Ly5MVTInouX19f4uPjjQ4DqO1vFhMTQ58+fVpchtaajIwMjh49Sk1NjROjc77IyEiuu+46vvrqK0pLS11aV3BwMBMmTGDZsmVe0S9PeDdJzoQQHkFrzYkTJzCZTERFRRkdTpOqqqp46aWXPGZR7KqqKtLS0pgyZcpVDaCoX0Wgurqao0ePenwiMmnSJCorK/niiy9cXtf06dPJzMxkx44dLq9LXNskORNCeISzZ89SUlJCTEyMRzQRNuWbb74hPT0df39/o0MBavu+lZSUtKhJ82JBQUHExcVRWlpKVlZW0ycYKDo6mgEDBrBhwwaXz9U2bdo0fHx8+Oijj1xajxCSnAkhDFddXU1WVhZBQUFEREQYHU6TbDYba9euJT4+nsTERKPDAWqbNC0WC+PGjXNKeeHh4bRv3568vDwKCz17msmpU6cyb948fH19XVpPWFgYEydOZMmSJR7/RFF4N0nOhBCGq66uxmKxePycZvW+//578vPzuemmmzwm3tWrV3PjjTc6df3RmJgYYmNjPX4EZ3R0NN26dXPLvZg5cybHjx/nu+++a/pgIVpIkjMhhOECAwPp1auXxy/TBLV941JTU4mKimLAgAFGhwPAiRMn2Lt3b4um0LgSpRTt27fHZDJRU1Pj0csXlZeXs2jRInbt2uXSeqZOnYqfnx+LFy92aT3i2ibJmRDCMFarlVOnTmGz2TzmCZQjpkyZwowZMzCZPOMtdPXq1UDLptBwhNaaw4cPc/ToUWw2m0vquFp+fn7s37+fNWvWuLSekJAQJk+ezMcff+yx3wvh/TzjnUUIcU3Kycnh5MmTXjGnVj2lFAMHDvSIdTTrrV69mri4OJKSklxSvlKK6OhoysrKOH78uEf2tzKZTIwbN46jR4+SkZHh0rpmzpzJyZMn2bRpk0vrEdcuSc6EEIYoKSkhLy+PyMhI2rRpY3Q4DsnOzmblypWUl5cbHYpdRUUF69atY/LkyS59+hgaGkp0dDRnz57lzJkzLqvnalx//fUEBAS4fFLaW265hcDAQGnaFC4jyZkQwu1sNhvHjx/H19eXmJgYo8NxWGpqKuvWrfOo5qwNGzZw/vx5brvtNpfX1aFDB0JDQ8nOzqa4uNjl9TWXv78/N954Izt27CA/P99l9QQFBXHrrbfyySefePxEvcI7SXImhHC7kydPUllZSVxcnFcs0QS1MW/bto0xY8YQFBRkdDh2K1euJCgoiDFjxri8rvoJaiMiIjx28MbYsWO58cYbXf5zdeedd5KXl8eGDRtcWo+4NklyJoRwu/DwcGJjYwkJCTE6FId9/vnn+Pn5MWHCBKNDsdNa89lnnzFx4kS3TYZrNpuJi4vDYrGgtfaop4gA7dq146677qJdu3YurWfy5MkEBwezZMkSl9Yjrk2SnAkh3Ka+I3lAQADt27c3OBrHZWdns337dsaOHetR/eO+//57cnJy3NKkeTGtNenp6Rw7dswjBwgcPXqUPXv2uKx8f39/pk2bxtKlSz16ihHhnSQ5E0K4zcmTJ8nIyPDIP+ZXYjabGTx4MOPHjzc6lAusXLkSpRQ333yz2+tWShEcHExRURG5ublur78pS5cuZfHixS59sjdz5kyKiopIS0tzWR3i2iTJmRDCLc6fP8/p06cxmUxeNacZQMeOHXnooYc8qq8Z1CZn119/PZGRkYbU3759e9q1a0dOTg7nzp0zJIbLGT9+PPn5+S6dlHb8+PG0a9dORm0Kp5PkTAjhcvWjMy0WC7GxsUaH0yzr168nLy/P6DAukZWVxffff29Ik2Y9pRRxcXEEBARw7Ngxly883hwDBgwgPDyc9evXu6wOX19f7rjjDlasWEFFRYXL6hHXHknOhBAud/r0acrLy+ncuTM+Pj5Gh+OwzMxMPvroI7Zs2WJ0KJf4/PPPAbj11lsNjcNsNtO1a1d8fX2xWq2GxtKQyWRizJgxHDlyhBMnTrisnjvvvJOSkhL7Kg1COIMkZ0IIl7JareTl5REWFkZoaKjR4ThMa82nn35KUFAQY8eONTqcSyxfvpxu3brRs2dPo0PBz8+PpKQkAgMDjQ7lAiNHjiQ8PNylTz6Tk5OJioqSpk3hVC5NzpRSk5RSh5RS6UqpJxvZr5RSr9Xt362UGnTRfrNS6nul1OeujFMI4Tpms5levXrRqVMno0NplgMHDnDw4EFuvvlmj5vT6+zZs3zxxRfccccdHtN/TymFzWYjKyvLpRPANkdAQADPPfccgwcPdlkdPj4+zJgxg88//5zz58+7rB5xbXFZcqaUMgN/AyYDvYBZSqleFx02GUisez0E/OOi/T8DDrgqRiGEaxUXF6O1xmKxeFVzps1mY9myZURERDBq1Cijw7nE8uXLqamp4Qc/+IHRoVxAKUV5eTknTpzwmCWuTCYTNpvNpSNK77zzTsrKyvjss89cVoe4trjyydlQIF1rnaG1rgIWA1MvOmYq8L6u9S0QqpTqCKCUigVuBv7pwhiFEC5y7tw5jhw54pGd6ZtSXV1Nly5dmDZtGhaLxehwLvHxxx8THx/PoEGDmj7YjZRSJCQkYDabycjI8JgJaj/88EP++Mc/umw+spEjRxIdHS0T0gqncWVyFgNkNfg6u26bo8f8P+B/gSv+diulHlJKbVNKbfPGPwJCtEbV1dVkZmbi7+9PRESE0eE0m5+fH7Nnz+a6664zOpRLnD17lnXr1vGDH/zAY5o0G7JYLCQkJFBRUUFWVlbTJ7jBddddx/nz5/nuu+9cUr7JZOKHP/whKSkpHjeliPBOrkzOGnvXuHjmyUaPUUrdApzRWm9vqhKt9Zta6yFa6yFGzfUjhPgvrTXHjx/HarWSkJCAyeRd44527NjB0aNHjQ7jslauXOmRTZoNhYSE0KFDB86ePesR02skJibSqVMn1q9f77IJkGfNmkVVVRWffvqpS8oX1xZXvmtmAw17AMcCJx085gbgNqVUJrXNoWOVUgtdF6oQwlny8/M5d+4cMTExHjd6rynl5eUsWrSIlStXGh3KZdU3aQ4ZMsToUK4oOjqapKQk/Pz8jA4FpRTjxo3j1KlTHDjgmm7M1113HV27duWDDz5wSfni2uLK5GwrkKiUSlBK+QIzgYvf8VYCc+pGbQ4HzmmtT2mtn9Jax2qt4+vO+0JrfbcLYxVCOElAQADh4eFERUUZHUqzpaWlUVpayu233250KI2qXypoxowZHtmk2ZBSCn9/f7TWFBYWGt7/bMiQIbRt29ZlTZtKKWbPns369es5ffq0S+oQ1w6XJWda6xrgUWANtSMuP9Ja71NKPaKUeqTusBQgA0gH3gJ+4qp4hBCuVd9c1KZNG+Lj4z0+ebjYuXPnSEtLY8iQIcTHxxsdTqNWrFhBdXU1M2bMMDoUh5WVlZGRkcHJkxc3nLiXxWLh5z//OXPmzHFZHbNmzcJms/HRRx+5rA5xbVDetgDxlQwZMkRv27bN6DCEuOZorcnMzPTK5ZnqffDBB2zcuJHf/e53HvvUb9KkSRw6dIiMjAyvSn6PHz9Ofn4+iYmJhISEGB0O1dXVLhuFO2jQIHx9ffn2229dUr5oXZRS27XWl/RR8K6eukIIj5SXl8fZs2cxm81Gh9JikZGR3HTTTR6bmJ0+fZq0tDRmz57tVYkZQKdOnfD39yczM5OamhpDY8nIyOCpp54iMzPTJeXPnj2b7777zqMHlQjPJ8mZEOKqlJSUkJWVRdu2benQoYPR4bTYhAkTmDZtmtFhXNaSJUuw2WzcddddRofSbCaTiYSEBGpqasjMzHTZiElHdOzYEZvNxvLly11S/syZM1FK8eGHH7qkfHFtkORMCNFilZWVHD16FH9/f6/sZwZw4sQJtmzZYniH9aYsWrSIAQMG0KvXxQuteIfAwEA6depERESEoT8nAQEBTJkyhQMHDrhk5GZsbCyjRo1i0aJFhiahwrtJciaEaLHy8nJMJhNdu3b1quWZ6mmt+fjjj/noo49cNnu8Mxw5coStW7dy993ePWg9MjKS0NBQAEMTl9GjRxMWFsayZctckpTPnj2bgwcPsnPnTqeXLa4NkpwJIVosNDSUPn364O/vb3QoLbJv3z4OHz7MzTff7NHXsGjRIpRSzJw50+hQnCIvL4+DBw8a9rTSYrFw2223ceLECQ4fPuz08u+44w4sFovMeSZaTJIzIUSzaK05duwYBQUFAF63AkA9m83Gp59+SkREBDfeeKPR4VyW1ppFixYxZswYYmIuXgHPO/n6+lJWVkZOTo5hMQwbNownnniCnj17Or3s8PBwJk2axIcffujxzeXCM3nnu6oQwhBaa7Kzszl79izV1dVGh3NVtm7dSnZ2NlOnTvXoJtmtW7eSnp7ulQMBLqdt27ZERUVx5swZw9aiNJlMdO/eHYDz5887vfzZs2eTk5PDxo0bnV62aP0kORNCOCw3N5czZ84QFRVF+/btjQ7nqgQGBjJo0CCPXwZp4cKF+Pn5cccddxgdilPFxMQQEBBAZmamoYn+zp07efLJJzlx4oRTy7311lsJCgqSpk3RIpKcCSEckp+fT05ODmFhYcTGxnrlyMyG+vbty8MPP+zRzbI1NTUsWbKEW265hbZt2xodjlPVT69hs9koLi42LI7ExEQCAgJ49913nZokBgUFMW3aND7++GOPHmwiPJPnvisJITxKVVUVwcHBxMXFeXViVl5ezpo1a6isrDQ6lCatW7eOM2fOtKomzYYCAgLo06cP4eHhhsUQFBTEnDlzOHnypNMXvJ89ezaFhYWsWbPGqeWK1k+SMyHEFdVPeRAdHU1iYqJHP2lyxNq1a1m2bJlXLE69cOFCQkNDmTJlitGhuEz9MkrFxcWUlZUZEkOfPn248cYbSUtL48iRI04rd8KECYSHh7No0SKnlSmuDd79LiuEcKnz58+zd+9e+x9Nb35iBlBUVMS6desYMmQIcXFxRodzRUVFRSxdupRZs2bh5+dndDguZbPZyMzM5NixY4aNbpwxYwaRkZFkZWU5rUyLxcKsWbNYvnw5hYWFTitXtH6SnAkhGlVWVsaRI0dQSnn0aMbm+Oyzz7BarR69TFO9Dz/8kIqKCn70ox8ZHYrLmUwm4uPjqaiocGpy1Bz+/v78+te/ZuzYsU4td+7cuVRWVspyTqJZJDkTQlyioqKCI0eOYDKZSExMxNfX1+iQrtqpU6fYvHkzo0ePJjIy0uhwmvT222/Tv39/Bg0aZHQobhESEkL79u3Jz8837ClTfRPr/v372b17t1PKHDhwIAMGDOCdd95xSnni2iDJmRDiAlVVVfZZ07t3795qmtS01vTp04ebb77Z6FCatGvXLrZv386PfvQjr29Kbo7o6GgCAwM5fvy4YdNr2Gw2Vq5cybvvvsvZs2edUub999/P9u3b2bVrl1PKE62fJGdCiAv4+PgQHBxMYmKiRy9p1FzR0dE8+uijtGnTxuhQmvT222/j5+fXakdpXk799BrR0dGGNaWbTCZ+9KMfYbPZ+Oc//4nVar3qMu+66y58fX159913nRChuBZIciaEAGrn1KqpqbH/gQwMDDQ6JKfQWpOSkkJRUZHRoTikoqKChQsXcvvttxMWFmZ0OG7n7+9PVFQUSinDBgdERkZy1113cfToUVatWnXV5YWHhzN16lQWLlzoFVO4CONJciaEwGq1cvjwYdLT0+1TZ7QWO3bsYMWKFezbt8/oUBzy6aefUlhYeE0MBLiS0tJS9uzZ45KllRwxdOhQRowYQUpKilMGKcydO5eCggKnz6UmWidJzoS4xlmtVo4cOUJFRQUdO3ZsVX2cKisr+fjjj4mJiWHEiBFGh+OQBQsW0LVrV6ePGvQ2/v7+KKXIyMigpqbGkBhmzpzJPffcQ2xs7FWXNWHCBDp16sQ//vEPJ0QmWjtJzoS4htlsNjIyMjh//jwJCQmtbomglJQUCgsLmT17tldMnrtlyxa++eYb5s+f7xXxupKPjw9dunShurqajIwMQ57o+vv7c8MNN6CUoqio6KpiMJvNzJs3jw0bNjhtJKhova7t334hrnHZ2dkUFxcTFxdHu3btjA7HqU6fPk1aWhojRoygW7duRofjkL/85S+EhIRw//33Gx2KR2jTpg2dO3empKSE7Oxsw+LIzc3lN7/5DRs2bLiqch588EECAgJ47bXXnBSZaK0kORPiGtahQwfi4uKIiIgwOhSnCwoKYtiwYUyfPt3oUBySk5PDRx99xI9+9COCg4ONDsdjREREEBUVhdVqNaw/ZFRUFImJiSxduvSq+p+FhYUxZ84cFi5cyKlTp5wYoWhtXJqcKaUmKaUOKaXSlVJPNrJfKaVeq9u/Wyk1qG57J6XUBqXUAaXUPqXUz1wZpxDXEq01hYWFaK3x9fVtlYkZQHBwMPfeey8hISFGh+KQv//971itVh599FGjQ/E4sbGxxMXFoZQyJEFTSnHffffRpk0b3nrrrasacfmLX/yC6upqXnnlFSdGKFoblyVnSikz8DdgMtALmKWU6nXRYZOBxLrXQ0B9T8ka4AmtdRIwHJjXyLlCiBY4deoUGRkZTptg09Pk5OTwyiuvkJ+fb3QoDisvL+eNN95g6tSpdOnSxehwPI5SCqUUlZWV7N+/n5KSErfH0KZNG+bOncuZM2dYvHhxi8vp2rUrs2fP5vXXX/eqn1HhXq58cjYUSNdaZ2itq4DFwNSLjpkKvK9rfQuEKqU6aq1Paa13AGitS4ADQIwLYxXimpCbm8upU6cIDw9vlXNoVVRU8MYbb3D69GmvWnLqn//8JwUFBTz22GNGh+LRzGYzWmvS09MpLS11e/09evRg8uTJKKWuanLap59+mvLycl544QUnRidaE1cmZzFAw8b5bC5NsJo8RikVDwwEvmusEqXUQ0qpbUqpbXl5eVcbsxCtVn5+PtnZ2YSGhtqbiFoTrTULFy7kzJkzPPDAA17TnFlRUcELL7zAqFGjGDVqlNHheDQfHx+6d++OxWLhyJEjhiRot912G3PmzMFsNre4jKSkJO677z7++te/kpmZ6bzgRKvhyuSssXf+izsLXPEYpVQbYCnwmNa6uLFKtNZvaq2HaK2HeMNixkIYoaamhqysLIKDg0lISGh1iRlAamoqW7duZerUqfTo0cPocBz25ptvcurUKX7729+2yvvibL6+vhckaO6epLb+HmVnZ/POO++0eA623/3ud5hMJp5++mlnhidaCVcmZ9lApwZfxwInHT1GKWWhNjFbpLVe5sI4hWj16p84dO3atVXOn1VdXc3WrVsZOnQoN910k9HhOKy+aWv06NGMGTPG6HC8hq+vLz169KBt27aGrf965swZvvvuO1asWNGi82NjY/nFL37Bhx9+eNVTdIjWx5Xv0luBRKVUglLKF5gJXLxuxUpgTt2ozeHAOa31KVX70eRt4IDW+lUXxihEq1ZSUmLvdBwUFHRVTTGezGKx8Itf/II5c+Z4VfL55ptvcvr0aX77298aHYrXsVgsdOnSBbPZjM1mIy8vz60jOQcNGsSoUaNYu3Ytu3btalEZTz31FAkJCfzkJz+hoqLCyREKb+aydzGtdQ3wKLCG2g79H2mt9ymlHlFKPVJ3WAqQAaQDbwE/qdt+A3APMFYptbPuNcVVsQrRGp0/f5709HRyc3MNW0Da1XJycnjvvfeoqqoiICAAi8VidEgOKy0t5cUXXyQ5OZnk5GSjw/FqBQUFnDhxgvT0dKqrq91W7w9+8AM6d+7M22+/TU5OTrPPDwgI4O9//zsHDx7kmWeecUGEwlu59COm1jpFa91da91Va/183bbXtdav1/1fa63n1e3vq7XeVrd9k9Zaaa37aa0H1L1SXBmrEK1JeXk5R44cwcfHh8TERK96muSo/Px8FixYwP79+w1bHPtqvPDCC5w+fZrnn3/e6FC8XkREhH0lgQMHDrhtoICvry8/+clP8Pf3JzU1tUVlTJo0iR//+Me8+uqrfPHFF06OUHgrZdSMy64wZMgQvW3bNqPDEMJQ5eXlHD58GKUUPXr0wM/Pz+iQnK6wsJCXX36ZsrIyfv7zn9OpU6emT/IgR48epVevXvzwhz/k3//+t9HhtBplZWVkZGRQWVlJfHw84eHhbqk3NzeX8PBwfHx8WnR+WVkZAwcOpKysjN27d7e6pdTE5Smltmuth1y8vfV9nBbiGlc/QWdiYmKrTMyKi4v585//TGlpKfPnz/e6xAzgiSeewGKx8Mc//tHoUFqVwMBAkpKSCA8Pp02bNm6rt3379vj4+HD+/Hk++eSTZjetBgYGsmjRIk6fPs2Pf/xjw5apEp5DkjMhWon6STGjoqLo3bs3AQEBBkfkGkVFRVRVVfHoo4+SkJBgdDjNtnbtWlasWMEzzzxDdHS00eG0Omazmfj4ePz8/NBak5mZSVFRkVvqPnToEGlpabz++uvNTtCGDBnCs88+y5IlS/j73//uogiFt5BmTSFagcLCQk6cOEFiYiKBgYFGh+MSVVVV9ln/q6urvarzf7365iur1cq+ffta5ZNNT1JTU8Phw4cpLy8nPDycTp06uXzE8ldffcWiRYvo06cPDz/8cLNWqrDZbEydOpU1a9bw1VdfMXz4cBdGKjyBNGsK0QpprTl9+jQZGRn4+fl5ZcLiiOLiYl588UV7p2tvvc6nnnqKw4cP88Ybb0hi5gY+Pj707NmTDh06UFBQwP79+10+WGDUqFHcdddd7Nu3j1dffbVZ64CaTCbef/99OnXqxIwZMzhz5owLIxWeTJIzIbxUTU0NGRkZ5OTk0K5dO/us6a1NYWEhr7zyCmfOnCEuLs7ocFrsiy++4LXXXuOnP/0p48aNMzqca4bJZCImJsa+akRGRobLp5YZNWoUDz/8MGVlZc1eg7Ndu3YsXbqUgoICZs2a1eIVCIR3k2ZNIbzUyZMnOX36NDExMURFRbXKpX8KCgr485//THFxMT/96U9JTEw0OqQWOXfuHP369cPf35/vv/++1TY9ezqr1UplZSWBgYForamsrHTpCgNWqxWz2YzVaiU3N7dZfQzfffdd5s6dy5NPPikLpLdil2vWbNm4XyGEIWpqaqiqqiIwMJAOHToQGhraav/QV1VV8dJLL1FRUcHjjz/ulZ3/obbp+cc//jHZ2dl8/fXXrfZ+eQOz2Wz//ufm5nLy5EliY2OJjIx0yYeb+v5tq1atYs2aNcyYMYPk5GSH6rr//vv55ptvePHFF+nfvz8zZ850enzCc0lyJoQXqF+e5vTp05jNZnr37o3JZGrVf+h9fX2ZNm0anTt39upRjS+//DIffvghf/jDHxg2bJjR4Yg64eHhlJSUkJWVxblz54iLi2tW5/3mGDt2LMePH2fx4sUcOXKEe+65x6HR1AsWLODAgQPcd999JCQkyM/PNUSaNYXwYFarlYKCAk6fPk11dTXBwcHExsa22qSsqqqKjz/+mN69ezNgwACjw7lqqampTJkyhR/84AcsXry4VTY9ezOtNfn5+WRnZ6OUIiEhgbZt27qkLpvNZp9GJSIigocffpjY2Ngmz8vLy2PYsGGUlZWxZcsWOnfu7JL4hDFktKYQXqT+Q1NxcTFZWVn4+vrSvXt3unfv3moTs0OHDvH73/+er776qkXrFHqagwcPMnPmTPr168c777wjiZkHUkoRGRlJUlIS/v7+LZ7h3xEmk4lJkybxxBNPYLPZHP55iIyM5PPPP6e8vJybb76ZgoICl8UoPIc8ORPCQ1RVVXH27FnOnj1L27ZtiYmJQWtNWVkZQUFBRofnMrm5uaxYsYLt27cTERHBPffcQ8+ePY0O66ocP36ckSNHUllZyZYtW4iPjzc6JNEErbU9YTp58iTBwcEEBwe7pK76gQJQ2x+tf//+TT5FW79+PTfffDN9+/Zl3bp1LnvCJ9xLBgQI4aEKCgrIz8+3z78UFBRk74+ilGrViRlAdnY2e/fu5eabb2bSpEku6/fjLseOHWP8+PGUlJTw5ZdfSmLmJeoTM6vVytmzZzl16hQRERFER0c7fYqa+sSsuLiYDRs2sGrVKiZNmsTkyZMvW9e4ceP45JNPuP3227n55ptZs2ZNq39vuJbJkzMh3Mxms1FaWkpISAhQuwh2/QzmYWFhrX5y0rNnz5KWlkbbtm2ZNGkSWmtKS0td9pTCnb7//ntuvfVWysrKSE1NZejQoUaHJFrAarVy8uRJzpw5g8lkomPHjkRGRrpkdYHS0lKWLFnCli1biIqK4q677rrik+NPPvmEO++8kxEjRrBy5UrCwsKcHpNwn8s9OZPkTAg3qG+ezM/P5+zZs9hsNnr37o2/vz9WqxWTydTq+yTl5uayZs0avvnmGwDGjBnDD3/4Q4Ojcp4PPviABx54gPDwcFatWkW/fv2MDklcpYqKCrKzsykpKaFv3774+Phc0PzpTPv37+eDDz7g/Pnz/OEPf7jiaM5PPvmEu+++m/j4eFavXu2108wISc6EMExZWRnHjh2joqICk8lEu3btCAsLIzg4uNUnZPXWrl3LsmXL8PHxYeTIkUycOLHVfOKvqKjg6aef5s9//jM33ngjH3/8Me3btzc6LOFEDdd1PXToEH5+fkRERBAUFOTU3+GqqipOnjxJfHw8NpuNnTt3MmDAAEymS8fubdy4kalTp+Lr68uyZcu4/vrrnRaHcB9JzoRwE621fT29kJAQampqOHr0KGFhYYSFhbl84WVPYLVa2blzJ506dSIqKopjx46xc+dOxo0bZ2/ObQ3+85//8OCDD3LkyBHmzZvHq6++6vV95sTl2Ww2srKy7E+/AwICiIiIICwszOkjPXfs2MEbb7xBp06d+MEPfmBffqqhAwcOcMstt5CZmcmvfvUrnnnmGZeOOBXOJ8mZEC5WVVVl79xfVVVFcHAw3bt3Nzost8rPz+e7775j06ZNnD17lkmTJnH77bcbHZbTHTx4kOeff56FCxfSpUsXXn/9dSZMmGB0WMJN6gcN5OfnU1ZWRnx8POHh4VitVpRSjT7pai6tNVu3buXTTz/l7Nmz9O/fn+nTp9OhQ4cLjqtf2uz9999n+PDh/OMf/2gVcwReKyQ5E8KFsrOzyc3NBSA4OJiIiAhCQ0Od8ibtDbTW/P3vf2f37t0A9OjRg7Fjx9KvX79W8z2w2Wxs2rSJBQsWsHTpUvz9/Zk/fz6//vWvW+3cc6JpZWVl+Pn5YTab7UtChYaG0q5dO0JCQq7657+qqor169ezevVqwsPD+fWvf91oU+rixYuZN28ehYWF3HfffTz33HNevbLGtUKSMyGcRGtNcXExZ8+epVOnTvj4+HD27FnKy8uJiIho9aMtofYP0q5duzh69Ch33XUXSilWrlyJ2Wxm+PDhhIeHGx2iU2it2blzJx988AGLFy8mOzubkJAQHn30UR577DEiIyONDlF4kPPnz5Ofn09hYaH9KVpISAhdu3a96r5pxcXFFBYWEhcXR0VFBf/617+44YYbSEpKsneVKCws5A9/+AOvvfYaSinmzJnD448/TlJSkjMuT7iAJGdCXAWr1UpRURHnzp2juLjYPolk165dW8UUEI4oLy9n586dbN++nf3792O1WgkLC+Opp55qVf3IANLT0/nwww/54IMPOHjwID4+PkyaNInZs2dz2223yfxS4orqp8s5d+4cNTU19tGUGRkZ9rkLAwIC7KsSNDdxO3bsGH/7298oKSkhJCSEfv360bt3b3r37o2fnx8ZGRn88Y9/5P3336eiooIJEyZw7733Mm3aNPnZ9TCSnAnhAK01NTU1lJeXU1ZWRkBAAG3btqWqqoo9e/bg4+ND27ZtCQ0NdUqThafLy8vDz8+PkJAQtm7dyj//+U/CwsIYPHgwgwcPJj4+vtWMOD116hQfffQRH3zwAVu2bAFg9OjRzJo1ixkzZrSap4HCOBkZGZSUlFBTU2PfFh4ebp+oODMzE7PZjMViwcfHBx8fHwICAvDz87Mv6Vb/+1ZTU8PevXv57rvv2L9/PxUVFTz//PNERESwa9cu0tPTCQoKYuPGjXz88cccOXKENm3aMGXKFPuEz1FRUW7/HogLSXImRB2tNdXV1VRVVQHQpk0bAI4cOUJZWdkFb5yRkZH2hYbrk7XWkoxczGazkZ2dzYkTJzh+/DiHDh0iNzeX6dOnc9NNN1FZWWkf5t8avgdaaw4fPsxnn33G8uXL+frrr9FaM3DgQGbPns2dd95Jp06djA5TtDL17z8VFRVUVFTg6+tLaGgoNpuN/fv3U11djc1msx/fvn17YmNjsVqt7Nq1Cx8fHywWC76+vvZzAwICOHbsGJ07d8bX15fPPvuM1NRUrFarvRxfX18qKyv57LPP8PHxwc/Pj7CwMPr27cuIESMYMWIEPXv2vCZGk3sSQ5IzpdQk4C+AGfin1vrFi/aruv1TgDLgPq31DkfObYwkZ62b1hqtNTabDavVan8Dq5+ssbi4mMrKSmw2m/0Yi8Vin3Pq6NGjlJaWXpB8NRxRmZGRgdlsJiAgwP7y1mHpWmsqKyvtS0JFREQAtXMjFRUVUVpayvnz5yktLaVbt27ccsstVFdX87Of/Qyr1UpgYCAJCQn06dOH/v37e/VTo8rKSgoKCsjJySE9PZ309HS2bdvG119/TX5+PgADBgxg6tSp3HnnndI/RxjOarVSU1NDTU2NPZGyWq2cOnWKmpoa+4fLqqoqYmJiiIqKory8nP379wPYk7f6RLB+ebhx48ZhNpv585//TGZmpr2+srIyTp8+zaZNm+jVqxd9+/alS5cudO3albi4OOLi4ujYsaPXvh96MrcnZ0opM3AYmABkA1uBWVrr/Q2OmQL8lNrkbBjwF631MEfObUxrSc4auydKqUu2N3zMXb//cufW72/4iaxe/ez0Nput0TLMZjNKKfsbRv0x9a/AwECUUlRWVlJZWXnJ/nbt2qGUorS0lPLy8gv2Afah4Xl5eRQXF1+QXJlMJvtSJkePHqWoqOiC2Hx9fenbty8Ahw8fts8vVn/dgYGB9vNzcnKoqanBYrHY37z8/f2d2oH/4mur/37Xr5dXVVVlTyytVqv9k227du2A2qkoysvL7ftsNhs+Pj72Piv79++noKCAyspKqqqqqKysJCgoiIkTJwLw17/+lePHj3P+/Hl72b169eJnP/sZAE8//TQFBQUEBgbSpk0bgoKC6Nu3LzfffDMAe/fupX379kRERLjl6Vj9z2TDhLuyspLy8vJLXhUVFZfdXlZWRmFhIWfPnqWgoOCC1/nz5y+pNzExkRtuuIERI0Zw0003ERcX5/JrFcLZGv4NqK6upqioyJ601SdwnTp1om3btpw7d4709PRLyigqKmL//v3U1NQQExPD6dOn8fHxwWw2Y7Va7e+rpaWlVFdXExAQQGxsrL3ZtbCwEF9fXzp06EBcXBzBwcFUVFTg5+dn71cXFBREWFiYvb9bYWGh/e9O/d8Xf39//P390VrbJ+w2m834+PhgMpmwWCyYzeYL/o41fI+q/zvnbYxY+HwokK61zqgLYDEwFWiYYE0F3te1P2HfKqVClVIdgXgHznW7mpoa9uzZY/+6/hejY8eOdOzYkaqqKvbu3XvJebGxsZd8smkoLi6OiIgIzp8/z8GDBy/Zn5CQQFhYGCUlJRw5cuSS/d26dbP/8h09evSS/d27dyc4OJizZ89e8GmpXlJSEoGBgeTn55OVlXXJ/j59+uDn50deXh45OTmX7O/Xrx8Wi4X8/HxOnz59yf7Q0FCUUhQWFnLmzJlL9rdv396e3DX8pfT19b3gk1q7du0IDAzEbDZjMpkwmUwX7K/vt1F//sW/qDExMZfU3VzLly9n/fr1lySgf/vb3zCZTHzwwQd89dVXF5zj6+vLggULAPj3v/9t789ULyQkhJdeegmoHQ7f8GcMICoqit///vcApKamcujQIfs+k8lEt27d7MlZTEwMbdu2JSgoiKCgINq0aXPBiMJnnnnGPuy/MX369GnJt6VJ06ZNIy0tzZ6A1SdjzmIymQgNDSU8PJzw8HCio6Pp27ev/evw8HA6duxIt27dSEhIkKkvRKvQ8D3OYrFccfRwUFAQ3bp1s39ArH8y17t3b8aNG0dRUREnTpwgMTHxgg/xFouFEydOEBMTw3XXXXdJuUuWLOHcuXMEBwfTpUuXS/YvXLiQsrIy4uLiuOmmmy7Z/+6771JdXU3Xrl0ZN27cBfu01rz11lsA9OzZkxtuuOGC666uruZf//oXAPfee689uat/bykrK2Px4sUA3H///VgsFnu/YqhtbVm+fDlKKe67774L3he7d+9u6OAJVz45mwFM0lo/UPf1PcAwrfWjDY75HHhRa72p7uv1wC+pTc6ueG6DMh4CHqr7sgdwCIgA8l1yYcLZ5F55D7lX3kXul/eQe+U9nH2v4rTWl2TVrnxy1tjzxYszwcsd48i5tRu1fhN484JCldrW2GNC4XnkXnkPuVfeRe6X95B75T3cda9cmZxlAw2HOsUCJx08xteBc4UQQgghWh1XTtK0FUhUSiUopXyBmcDKi45ZCcxRtYYD57TWpxw8VwghhBCi1XHZkzOtdY1S6lFgDbXTYbyjtd6nlHqkbv/rQAq1IzXTqZ1K4/4rnduM6t9s+hDhIeReeQ+5V95F7pf3kHvlPdxyr1rVJLRCCCGEEN6uda89I4QQQgjhZSQ5E0IIIYTwIK0qOVNK/V4ptVsptVMptVYpFd1g31NKqXSl1CGl1KUz4Qm3Ukq9pJQ6WHe/PlVKhTbYJ/fKgyilfqCU2qeUsimlhly0T+6Vh1FKTaq7H+lKqSeNjkf8l1LqHaXUGaXU3gbbwpRSaUqpI3X/tjMyRlFLKdVJKbVBKXWg7v3vZ3Xb3XK/WlVyBrykte6ntR4AfA78GkAp1YvaEZ+9gUnA3+uWiBLGSQP6aK37UbtU11Mg98pD7QWmAxcsfSD3yvPUff//BkwGegGz6u6T8AzvUfu70tCTwHqtdSKwvu5rYbwa4AmtdRIwHJhX97vklvvVqpIzrXVxgy+D+O/EtVOBxVrrSq31MWpHhw51d3ziv7TWa7XW9SuQf0vtXHYg98rjaK0PaK0PNbJL7pXnsS+bp7WuAuqXvhMeQGv9FXD2os1TgX/V/f9fwDR3xiQap7U+pbXeUff/EuAAEIOb7lerSs4AlFLPK6WygLuoe3JG7Te04aKR2XXbhGeYC6yu+7/cK+8h98rzyD3xPu3r5vek7t8og+MRF1FKxQMDge9w0/1y5QoBLqGUWgd0aGTX/2mtV2it/w/4P6XUU8CjwG9oxnJQwnmauld1x/wftY+PF9Wf1sjxcq9czJF71dhpjWyTe2UsuSdCOJFSqg2wFHhMa13ccLF5V/K65ExrPd7BQz8AVlGbnDmylJRwsqbulVLqXuAWYJz+74R7cq8M0Izfq4bkXnkeuSfeJ1cp1VFrfUop1RE4Y3RAopZSykJtYrZIa72sbrNb7leratZUSiU2+PI24GDd/1cCM5VSfkqpBCAR2OLu+MR/KaUmAb8EbtNalzXYJffKe8i98jyy9J33WQncW/f/e4HLPakWbqRqH5G9DRzQWr/aYJdb7lerWiFAKbUU6AHYgOPAI1rrnLp9/0dt36Yaah9Prr5sQcLllFLpgB9QULfpW631I3X75F55EKXU7cACIBIoAnZqrW+q2yf3ysMopaYA/4//Ln33vLERiXpKqQ+BZCACyKW2ZWc58BHQGTgB/EBrffGgAeFmSqmRwEZgD7U5BcDT1PY7c/n9alXJmRBCCCGEt2tVzZpCCCGEEN5OkjMhhBBCCA8iyZkQQgghhAeR5EwIIYQQwoNIciaEEEII4UEkORNCCCGE8CCSnAkhhBBCeJD/D5HivHe9NMk2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "np.random.seed(123)\n",
    "\n",
    "n1 = np.random.normal(4, 3, 30000)\n",
    "n2 = np.random.normal(1, 4, 30000)\n",
    "n_diff = n2 - n1\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "sns.distplot(n1, hist=False, label=\"$N(4,3^2)$\", color=\"0.0\", kde_kws={\"linestyle\":linestyle[0]})\n",
    "sns.distplot(n2, hist=False, label=\"$N(1,4^2)$\", color=\"0.4\", kde_kws={\"linestyle\":linestyle[1]})\n",
    "sns.distplot(n_diff, hist=False,\n",
    "             label=f\"$N(-3, 5^2) = N(1,4^2) - (4,3^2)$\", color=\"0.8\", kde_kws={\"linestyle\":linestyle[1]})\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:32.141048Z",
     "start_time": "2023-09-01T17:14:32.137649Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% CI for the differece (short email - no email):\n",
      "(0.01023980847439844, 0.15465380854687816)\n"
     ]
    }
   ],
   "source": [
    "diff_mu = short_email.mean() - no_email.mean()\n",
    "diff_se = np.sqrt(no_email.sem()**2 + short_email.sem()**2)\n",
    "\n",
    "ci = (diff_mu - 1.96*diff_se, diff_mu + 1.96*diff_se)\n",
    "print(f\"95% CI for the differece (short email - no email):\\n{ci}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:32.214519Z",
     "start_time": "2023-09-01T17:14:32.142862Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(diff_mu - 4*diff_se, diff_mu + 4*diff_se, 100)\n",
    "y = stats.norm.pdf(x, diff_mu, diff_se)\n",
    "\n",
    "plt.figure(figsize=(10,3))\n",
    "plt.plot(x, y, lw=3)\n",
    "plt.vlines(ci[1], ymin=0, ymax=4, ls=\"dotted\")\n",
    "plt.vlines(ci[0], ymin=0, ymax=4, ls=\"dotted\", label=\"95% CI\")\n",
    "plt.xlabel(\"Diff. in Conversion (Short - No Email)\\n\")\n",
    "plt.legend()\n",
    "plt.subplots_adjust(bottom=0.15)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Null Hypothesis\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:32.219374Z",
     "start_time": "2023-09-01T17:14:32.215971Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% CI 1% difference between (short email - no email):\n",
      "(0.00023980847439844521, 0.14465380854687815)\n"
     ]
    }
   ],
   "source": [
    "# shifting the CI\n",
    "diff_mu_shifted =  short_email.mean() - no_email.mean() - 0.01 \n",
    "diff_se = np.sqrt(no_email.sem()**2 + short_email.sem()**2)\n",
    "\n",
    "ci = (diff_mu_shifted - 1.96*diff_se, diff_mu_shifted + 1.96*diff_se)\n",
    "print(f\"95% CI 1% difference between (short email - no email):\\n{ci}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Test Statistic\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:32.224419Z",
     "start_time": "2023-09-01T17:14:32.220897Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2379512318715364"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_stat = (diff_mu - 0) / diff_se\n",
    "t_stat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    " \n",
    "## P-values\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:32.319306Z",
     "start_time": "2023-09-01T17:14:32.231500Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd462fd6650>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-4, 4, 100)\n",
    "y = stats.norm.pdf(x, 0, 1)\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(x, y, lw=2)\n",
    "plt.vlines(t_stat, ymin=0, ymax=0.1, ls=\"dotted\", label=\"T-Stat\", lw=2)\n",
    "plt.fill_between(x.clip(t_stat), 0, y, alpha=0.4, label=\"P-value\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:32.323269Z",
     "start_time": "2023-09-01T17:14:32.320788Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P-value: 0.025224235562152142\n"
     ]
    }
   ],
   "source": [
    "print(\"P-value:\", (1 - stats.norm.cdf(t_stat))*2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Power\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:32.327853Z",
     "start_time": "2023-09-01T17:14:32.324718Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7995458067395503"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.cdf(0.84)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample Size Calculation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:32.332472Z",
     "start_time": "2023-09-01T17:14:32.329120Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "103.0"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# in the book it is np.ceil(16 * no_email.std()**2/0.01), but it is missing the **2 in the denominator.\n",
    "np.ceil(16 * (no_email.std()/0.08)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-01T17:14:32.338471Z",
     "start_time": "2023-09-01T17:14:32.334244Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cross_sell_email\n",
       "long        109\n",
       "no_email     94\n",
       "short       120\n",
       "dtype: int64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.groupby(\"cross_sell_email\").size()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Key Ideas\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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